! CONTEMPORARY MATHEMATICS

162

Classification of Algebraic Varieties

Algebraic Geometry Conference on Classification of Algebraic Varieties

May 22-30, 1992 University of L' Aquila

L' Aquila , Italy

Ciro Ciliberto E. Laura Livorni

Andrew J. Sommese Editors

Recent Titles in This Series

162 Ciro Ciliberto, E. Laura Livomi, and Andrew J. Sommese, Editors, Classification of algebraic varieties, 1994

161 Paul A. Schweitzer, S. J., Steven Hurder, Nathan Moreira dos Santos, and Jose Luis Arraut, Editors, Differential topology, foliations, and group actions, 1994

160 Niky Kamran and Peter J. Olver, Editors, Lie algebras, cohomology, and new applications to quantum mechanics, 1994

159 William J. Heinzer, Craig L. Huneke, and Judith D. Sally, Editors, Commutative algebra: Syzygies, multiplicities, and birational algebra, 1994

158 Eric M. Friedlander and Mark E. Mahowald, Editors, Topology and representation theory, 1994

157 Alfio Quarteroni, Jacques Periaux, Yuri A. Kuznetsov, and Olof B. Widlund, Editors, Domain decomposition methods in science and engineering, 1994

156 Steven R. Givant, The structure of relation algebras generated by relativizations, 1994 155 William B. Jacob, Tsit-Yuen Lam, and Robert 0. Robson, Editors, Recent advances in

real algebraic geometry and quadratic forms, 1994 154 Michael Eastwood, Joseph Wolf, and Roger Zierau, Editors, The Penrose transform and

analytic cohomology in representation theory, 1993 153 RichardS. Elman, Murray M. Schacher, and V. S. Varadarajan, Editors, Linear algebraic

groups and their representations, 1993 152 Christopher K. McCord, Editor, Nielsen theory and dynamical systems, 1993 151 Matatyahu Rubin, The reconstruction of trees from their automorphism groups, 1993 150 Carl-Friedrich Bodigheimer and Richard M. Hain, Editors, Mapping class groups and

moduli spaces of Riemann surfaces, 1993 149 Harry Cohn, Editor, Doeblin and modem probability, 1993 148 Jeffrey Fox and Peter Haskell, Editors, Index theory and operator algebras, 1993 147 Neil Robertson and Paul Seymour, Editors, Graph structure theory, 1993 146 Martin C. Tangora, Editor, Algebraic topology, 1993 145 Jeffrey Adams, Rebecca Herb, Stephen Kudla, Jian-Shu Li, Ron Lipsman, and Jonathan

Rosenberg, Editors, Representation theory of groups and algebras, 1993 144 Bor-Luh Lin and William B. Johnson, Editors, Banach spaces, 1993 143 Marvin Knopp and Mark Sheingorn, Editors, A tribute to Emil Grosswald: Number

theory and related analysis, 1993 142 Chung-Chun Yang and Sheng Gong, Editors, Several complex variables in China, 1993 141 A. Y. Cheer and C. P. van Dam, Editors, Fluid dynamics in biology, 1993 140 Eric L. Grinberg, Editor, Geometric analysis, 1992 139 Vinay Deodhar, Editor, Kazhdan-Lusztig theory and related topics, 1992 138 Donald St. P. Richards, Editor, Hypergeometric functions on domains of positivity, Jack

polynomials, and applications, 1992 137 Alexander Nagel and Edgar Lee Stout, Editors, The Madison symposium on complex

analysis, 1992 136 Ron Donagi, Editor, Curves, Jacobians, and Abelian varieties, 1992 135 Peter Walters, Editor, Symbolic dynamics and its applications, 1992 134 Murray Gerstenhaber and Jim Stasheff, Editors, Deformation theory and quantum

groups with applications to mathematical physics, 1992 133 Alan Adolphson, Steven Sperber, and Marvin Tretkoff, Editors, p-Adic methods in

number theory and algebraic geometry, 1992 132 Mark Gotay, Jerrold Marsden, and Vincent Moncrief, Editors, Mathematical aspects of

classical field theory, 1992

(Continued in the back of this publication)

http://dx.doi.org/10.1090/conm/162

Classification of Algebraic Varieties

CoNTEMPORARY MATHEMATICS

162

Classification of Algebraic Varieties Algebraic Geometry Conference on Classification of Algebraic Varieties

May 22-30, 1992 University of L' Aquila

L' Aquila, Italy

Ciro Ciliberto E. Laura Livorni

Andrew J. Sommese Editors

American Mathematical Society Providence, Rhode Island

EDITORIAL BOARD Craig Huneke, managing editor

Clark Robinson J. T. Stafford Linda Preiss Rothschild Peter M. Winkler

The Algebraic Geometry Conference on Classification of Algebraic Varieties was held May 22-30, 1992, at the University of L'Aquila, L'Aquila, Italy, with support provided by the following institutions: Ambasciata di Spagna; Azienda Autonoma del Soggiorno e Turismo di L'Aquila; Comune di L'Aquila; C.N.R. (Consiglio Nazionale delle Ricerche); Consiglio Regionale di L'Aquila; Dipartimento di Matematica dell'Universita degli Studi di L'Aquila; Dipartimento di Matematica dell'Universita degli Studi di Pisa; Dipartimento di Matematica dell'Universita degli Studi di Roma II; Fondazione Cassa di Risparmio della Provincia di L'Aquila; G.N.S.A.G.A (Gruppo Nazionale perle Strutture Algebriche e Geometriche e loro Applicazioni); Universita degli Studi di L' Aquila.

1991 Mathematics Subject Classification. Primary 14-06.

Library of Congress Cataloging-in-Publication Data Algebraic Geometry Conference on Classification of Algebraic Varieties (1992: University of L'Aquila)

Classification of algebraic varieties: proceedings of the Algebraic Geometry Conference on Classification of Algebraic Varieties, May 22-30, 1992, University ofL'Aquila, L'Aquila, ltaly/Ciro Ciliberto, E. Laura Livorni, Andrew J. Sommese, editors.

p. em. -(Contemporary mathematics; v. 162) ISBN 0-8218-5179-9 (acid-free) 1. Algebraic varieties-Classification-Congresses. I. Ciliberto, D. (Ciro), 1950-. II. Livorni,

E. L. (Elvira Laura), 1951-. III. Sommese, Andrew John. IV. Title. V. Series: Contemporary mathematics (American Mathematical Society); . QA564.A37 1992 516.3'5-dc20

93-44549 CIP

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Contents

Introduction 1x

List of Participants xi

List of Seminars XlX

On curves in C(2) generating proper abelian subvarieties of J(C) A. ALZATI AND G. PIROLA 1

Lefschetz type results for proper intersections L. BADESCU 19

Some effects of the spectral values on reductions M. C. BELTRAMETTI AND A. J. SOMMESE 31

Surfaces in P4 and deficiency modules G. BOLONDI 49

The class C is not stable by small deformations. II F. CAMPANA 65

Surfaces with K 2 = x = 2 and special nets of quadrics in 3-space F. CATANESE, P. CRAGNOLINI, AND P. OLIVERIO 77

Non-isomorphic curves of genus four with isomorphic (non-polarized) jaco-bians

C. CILIBERTO AND G. VAN DER GEER 129

Deformations of symmetric products of curves B. FANTECHI 135

Q-acyclic surfaces and their deformations H. FLENNER AND M. ZAIDENBERG 143

On a question of J. Kollar A. GRASSI 209

Boundedness for some special families of embedded manifolds P. lONESCU AND M. TOMA 215

Generalized Euler sequence and toric varieties K. J ACZEWSKI 227

vii

viii CONTENTS

A generalized Teissier-Plucker formula S. L. KLEIMAN 249

Log surfaces of general type; some conjectures J. KOLLAR 261

On triple covers of pn as very ample divisors A. LANTER!, M. PALLESCHI, AND A. J. SOMMESE 277

Component numbers for torsion sections of semistable elliptic surfaces R. MIRANDA 293

Braid group techniques in complex geometry III: Projective degeneration of v3

B. MOISHEZON AND M. TEICHER 313

Braid group techniques in complex geometry IV: Braid monodromy of the branch curve 83 of V3 --+ CIP'2 and application to TI1 (CIP'2 - 83 , *)

B. MOISHEZON AND M. TEICHER 333

On the irregularity of cyclic coverings of the projective plane F. SAKAI 359

Counting rational points on cubic surfaces SIR P. SWINNERTON-DYER 371

Miyaoka-Yau inequality for normal surfaces and local analogues J. WAHL 381

Minimal models of Calabi-Yau threefolds P. M. H. WILSON 403

Introduction

The vitality of algebraic geometry belies its long history and great depth. This

is because of the ongoing wide ranging, interaction that algebraic geometry has with

the rest of mathematics.

This activity, was clear at the L'Aquila Conference, which was attended by

numerous mathematicians from all the word (see enclosed list of participants) and is

illustrated by the breadth of the problems treated in the seminars (see also the

enclosed list of seminars held during the Conference) and studied in the proceedings.

Just to mention a few of the topics in the proceedings, there are articles on:

• the topology of algebraic varieties and on braid groups,

• Riemann surfaces and their jacobians,

• projective classification theory,

• toric varieties,

• enumerative formulae,

• generalizations of Kahler differential geometry,

• the theory of algebraic surfaces, • the Calabi-Yau threefolds (of much current interest to physicists),

• the spectacular mathematics growing out of the work of Mori. The conference in L'Aquila was not only a place for fruitful mathematical

interaction, but was an occasion where old friendships were renewed and many new

friendships were made. The atmosphere was very stimulating and enjoyable.

The conference and this proceedings owe their great success to all who attended

for their active discussions and their endurance.

The editors

ix

List or participants

A. Alzati, Dipartimento di Matematica- Universita degli Studi di Milano - Via C.

Saldini 50 - 20133 MILANO - Italy. E-mail address: ALZATI @

UMIMAT.MAT.UNIMI.IT

M. Andreatta, Dipartimento di Matematica - Universita degli Studi di Trento -

38050 POVO - Trento - Italy. E-mail address: ANDREATTA @

TINCISCA.BITNET

E. Arbarello, Dipartimento di Matematica - Universita degli Studi di Roma I -

Piazzale Aldo Moro 5 - 00185 ROMA- Italy.

E. Arrondo, Departamento de Algebra Facultad de Matematicas - Universidad

Complutense - E 28040 MADRID - Spain. E-mail address: W 258 @

EMDUCM11.BI1NET

L. Blldescu, Institute of Mathematics of the Romania Academy- P.O. BOX 1-764,

Ro-70700- BUCHAREST- Romania

E. Ballico, Dipartimento di Matematica- Universita degli Studi di Trento - 38050

POVO - Trento - Italy. Fax number 0039-461881624. E-mail address:

BALLICO@ I1NCISCA. BI1NET

F. Bardelli, Dipartimento di Matematica - Universita degli Studi di Pisa - Via

Buonarroti 2 - 56127 PISA - Italy. E-mail address: BARDELL! @

DM.UNIPI.IT

M. A. Barja, Departamento Matematica Aplicada 1 - Etseib Universitat Politecnia

Catalunya- Diagonal647- BARCELONA- Spain.

I. Bauer, Dipartimento di Matematica - Universita degli Studi di Pisa - Via

Buonarroti 2 - 56127 PISA - Italy. E-mail address: BAUER @

BIANCHI.DM.UNIPI.IT

S. Bauer, Mathematisches Institut der UniversiUit - Universitat Gottingen -

Bunsenstrasse 3 - 5 - 3400 GOTTINGEN - Germany. E-mail address: BAUER

@ CFGAUSS. UNIMATH.GWDG.DE

xi

xii LIST OF PARTICIPANTS

M. C. Beltrametti, Dipartimento di Matematica - Universita degli Studi di

Genova - Via L. B. Alberti 4 - 16132 GENOVA - Italy. E-mail address:

MBELTRA@ IGECUNIV. CISI.UNIGE.IT

L. Berardi, Dipartimento di Energetica- Universita degli Studi di L'Aquila- 67100

L'AQUILA - Italy

M. Bertolini, Dipartimento di Matematica - Universita degli Studi di Milano - Via

C. Saldini 50 - 20133 MILANO - Italy. E-mail address: BERTOLINI @

UMIMAT.MAT.UNIMI.IT

G. M. Besana, Dipartimento di Matematica- Universita degli Studi di L'Aquila -

Via Vetoio, Loc. Coppito - 67100 L'AQUILA - Italy. E-mail address:

BESANA@ VXSCAQ.CINECA.IT

A. Biancofiore, Dipartimento di Matematica- Universita degli Studi di L'Aquila-

Via Vetoio, Loc. Coppito - 67100 L'AQUILA - Italy. E-mail address:

BIANCOFIORE@ VXSCAQ.CINECA.IT

G. Bolondi, Dipartimento di Matematica- Universita degli Studi di Trento - 38050

POVO- Trento- Italy. E-mail address: BOLONDI@ ITNCISCA.BITNET

G. Brown, Mathematics Institute- University of Warwick- COVENTRY CV4 7AL

-England E-mail address: GDB@ MATHS.WARWICK.AC.UK

A. Bruno, Dipartimento di Matematica- Universita degli Studi di Roma 1- Piazzale

Aldo Moro 5-00185 ROMA- Italy

F. Campana, Department de Mathematiques- Universite Nancy 1 - BP 239, 54506

V ANDOEIVRE CEDEX- France.E-mail address: CAMPANA@ IECH.FR

G. Casnati, Dipartimento di Matematica Pura ed Applicata- Universita di Padova-

Via Belzoni 7 - 35131 PADOVA - Italy. E-mail address: CASNATI@

PDMATl.UNIPD.IT

F. Catanese, Dipartimento di Matematica - Universita degli Studi di Pisa - Via

Buonarroti 2 - 56127 PISA - Italy. E-mail address: CATANESE @

ICNUVEVM.BITNET

C. Ciliberto, Dipartimento di Matematica-Universita degli Studi di Roma II- Via

della Ricerca Scientifica- 00133 ROMA -Italy. E-mail address: CILIBERTO

@ MAT.UTOVRM.IT

LIST OF PARTICIPANTS xiii

E. Colombo, Dipartimento di Matematica - Universita degli Studi di Milano - Via

C. Saldini 50 - 20133 MILANO - Italy. E-mail address: COLOMBO@

UMIMAT.MAT.UNIMI.IT

M. Cornalba, Dipartimento di Matematica- Universita degli Studi di Pavia- Strada

Nuova 65 - 27100 PAVIA - Italy. E-mail address: CORNALBA @

IPV85.UNIPV.IT

A. Corti, Scuola Normale Superiore di Pisa- Piazza dei Cavalieri 7 - 56127 PISA-

Italy. E-mail address: CORTI@ IPISNSVA.BI1NET

M. de Cataldo, Department of Mathematics - University of Notre Dame - Notre

Dame, Indiana 46556 - U.S.A. E-mail address: MARKAN @

CART AN.MATH.ND.EDU

S. Di Rocco, Department of Mathematics - University of Notre Dame - Notre

Dame, Indiana 46556 - U.S.A. E-mail address: SANDRADR @

CARTAN.MATH. ND.EDU

I. Dolgachev, Department of Mathematics - University of Michigan - ANN

ARBOR, MI 48109 - U.S.A. E-mail address: IGOR_DOLGACHEV @

UM.UMICH.EDU

L. Ein, Department of Mathematics - University of Illinois at Chicago -

CHICAGO, IL 60680- U.S.A.

G. Ellingsrud, Matematisk Institutt - Universitet i Bergen - Allegaten 55 - 5007

BERGEN -Norway. E-mail address: GEIR@ MI.UIB.NO

F. Eugeni, Dipartimento di Energetica- Universita degli Studi di L'Aquila - 67100

L'AQUILA - Italy

M. L. Fania, Dipartimento di Matematica- Universita degli Studi di L'Aquila- Via

Vetoio, Loc. Coppito- 67100 L'AQUILA- Italy. E-mail address: FANIA@

VXSCAQ. CINECA.IT

B. Fantechi, Dipartimento di Matematica - Universita degli Studi di Trento - 38050

POVO- Trento- Italy. E-mail address: FAN1ECHI@ ITNCISCA.BI1NET

H. Flenner, Mathematisches Institut der Universitlit - Universitlit Gottingen -

Bunsenstrasse 3- 5 - 3400 GOTTINGEN - Germany. E-mail address:

HFLENNER@ CFGAUSS. UNI-MATH.GUDG.DE

xiv LIST OF PARTICIPANTS

P. Francia, Dipartimento di Matematica - Universita degli Studi di Genova - Via

L.B. Alberti 4 - GENOVA - Italy. E-mail address: FRANCIA @

IGECUNIV .BITNET

E. Frigerio, Dipartimento di Matematica - Universita degli Studi di Milano - Via

C. Saldini 50- 20133 MILANO- Italy

L. Guerra, Dipartimento di Matematica- Universita di Perugia - Via Vanvitelli 1 -

06100 PERUGIA- Italy

L. Gottsche, Max-Planck-Institut ftir Mathematik - Gottfried Claren Strasse 26 -

5300 BONN 3 - Germany. E-mail address: LOTHAR @ MPIM-

BONN.MPG.DBP.DE

K. Hulek, Institut ftir Mathematik- Universitat Hannover- Welfengarten 1 W 3000

HANNOVER 1 - Germany. E-mail address: KLAUS.HULEK@CDC2.C.

MA THEMATIK.UNI-HANNOVER.DBP.DE

P. Ionescu, Department of Mathematics -University of Bucharest -

St.ACADEMIEI, NR. 14- 70109 BUCHAREST- Romania

V. Iskovskih, Steklov Mathematician Institute- Vivilov Str. 42 - MOSCOW -

GSP 1.11 7 966 - RUSSIA

K. Jaczewski, Institute of Mathematics - Warsaw University - Banache 2 - 02-097

WARSZAWA- Poland. E-mail address: MAS 1@ PLEARN.BITNET

T. Kato, Katholieke Universiteit Leuven-Department of Mathematics-fac. of Sci. -

Yamaguchi University- YAMAGUCHI 753- JAPAN

Y. Kawamata, Department of Mathematics - University of Tokyo - Hongo

TOKYO 113 - Japan. E-mail address: KAWAMATA @ UTSS.S.U-

TOKYO.AC.JP

S. L. Kleiman, Department of Mathematics - 2-278 MIT - CAMBRIDGE -

Massachusetts 02139- U.S.A. E-mail address: KLEIMAN@ MATH. MIT.

EDU

J. Kollar, Department of Mathematics- University of Utah- SALT LAKE CITY-

UT 84112- U.S.A. E-mail address: Kollar@ MATH.UTAH.EDU

LIST OF PARTICIPANTS XV

K. Konno, College of General Education, Kyushu University, Ropponmatsu,

Chuo-ku, FUKUOKA 810, Japan. E-mail address: KONNO @

EMMY.DM.UNIP.IT

H. H. Lange, Mathematische Institut- University of Erlangen - Bismarckstr. 1 1/2

- 8520 ERLANGEN - Germany. E-mail address: LANGE @

CNVE.RRZE.UNI-ERLANGEN. DBP.DE

A. Lanteri, Dipartimento di Matematica - Universita degli Studi di Milano - Via C.

Saldini 50 - 20133 MILANO - Italy. E-mail address: LANTER! @

UMIMAT.MAT.UNIMI.IT

E. L. Livorni, Dipartimento di Matematica- Universita degli Studi di L'Aquila -

Via Vetoio, Loc. Coppito-67100 L'AQUILA-Italy. E-mail address:LIVORNI

@ VXSCAQ. CINECA.IT

A. Lopez, Dipartimento di Matematica - Universita degli Studi di Pavia - Strada

Nuova 65 - 27100 PAVIA- Italy. E-mail address: LOPEZ@ IPVIAN.BITNET

M. Manetti, Scuola Normale Superiore di Pisa- Piazza dei Cavalieri- 56126 PISA

-Italy. E-mail address: MANEm@ IPISNSV A.BITNET

N. Manolache, Institute of Mathematics of the Romania Academy- P.O. BOX 1-

764, Ro-70700 - BUCHAREST- Romania

G. Marini, Dipartimento di Matematica- Dottorato di Ricerca - Universita degli

Studi di Roma I - Piazzale Aldo Moro 5 - 00185 ROMA - Italy. E-mail

address: MARINI@ V AXRMA. INFN.IT G. Martens, Mathematisches Institut - University of Erlangen- Niirnberg -

Bismarckstr. 1 1/2 - 8520 ERLANGEN - Germany. E-mail address:

MARTENS@ CNVE.RRZE. UNI-ERLANGEN.DBP.DE

G. Megyesi, Trinity College Cambridge- CB2 ITQ- England. E-mail address: 9M

115 @ PHX.CAM.AC.UK.

K. Meeyoung, Department of Mathematics - University of Notre Dame - Notre

Dame, Indiana 46556 - U.S.A. E-mail address: MYING @

CARTAN.MATH.ND.EDU

xvi LIST OF PARTICIPANTS

R. Miranda, Department of Mathematics - Colorado State University - FORT

COLLINS, CO 80523 - U.S.A. E-mail address: MIRANDA @

RIEMANN.MATII.COLOSTATE. EDU

Y. Miyaoka, Department of Mathematics - Rikkyo University - Nishi-Ikeburo,

Toshimaku - 171 TOKYO -Japan

B. Moishezon, Department of Mathematics - Columbia University - NEW YORK,

N.Y. 10027 -U.S.A.

J. Murre, Department of Mathematics- University of Leiden -P.O. BOX 9512-

2300 RA LEIDEN - The Netherlands. E-mail address: MURRE @

RULCRI.LEIDENUNIV .NL

K. O'Grady, Institute for Advanced Study- Princeton- New Jersey 08540- U.S.A.

P. Oliverio, Dipartimento di Matematica - Universita della Calabria - 87036

ARCA V ACAT A DI RENDE (Cosenza) - Italy

C. Okonek, Mathematisches Institut - Universitlit Ziirich - Ramistrasse 74 - CH-

8001 Zurich- Switzerland

G. Ottaviani, Dipartimento di Matematica Applicata - Universita degli Studi di

Firenze- ViaS. Marta 3- 50139 Firenze- Italy.

M. Palleschi, Dipartimento di Matematica - Universita degli Studi di Milano - Via

C. Saldini 50 - 20133 MILANO - Italy. E-mail address: APELLES @

UMIMAT.MAT.UNIMI.IT

C. Pedrini,Dipartimento di Matematica - Universita degli Studi di Genova - Via

L.B. Alberti 4 - GENOVA - Italy. E-mail address: PEDRINI @

IGECUNIV.BTINET

T. Peternell, Mathematisches Institut - Universitlit Bayreuth- Universitlitsstr. 30,

Postf. 10 12 51 - 8580 BAYREUTH - Germany. E-mail address: THOMAS.

PETERNELL@ UNI-BA YREUTH.DBP.DE

R. Piene, Matematisk Institutt - University of Oslo - P.B. 1053 Blindern - 0136

OSLO- Norway. E-mail address: RAGNIP@ MATH.uio.no

G. Pirola, Dipartimento di Matematica - Universita degli Studi di Pavia - Strada

Nuova 65 - 27100 PAVIA - Italy. E-mail address: PIR023 @

IPVIAN.BTINET

LIST OF PARTICIPANTS xvii

M. Reid, Mathematics Institute- University of Warwick- COVENTRY CV4 7AL-

England. E-mail address: MILES@ MATHS.W ARWICK.AC.UK

I. Reider, Department of Mathematics - University of Oklahoma-NORMAN, OK

73019 - U.S.A.

J. Roberts, Department of Mathematics- University of Minnesota- 206 Church St.

S.E. - MINNEAPOLIS - MN 55455 - U.S.A. E-mail address: ROBERTS @

S6. MA TH.UMN.EDU

E. Rogora, Dipartimento di Matematica - Universita degli Studi di Roma I -

Piazzale AldoMoro 5 -00185 ROMA- Italy. E-mail address: OOTIORAT@

ITCASPUR

M. Rossi, Dipartimento di Matematica - Universita degli Studi di Firenze - Via

Buonarroti 2- Italy. E-mail address: UDINI@ IFliDG.BITNET

F. Russo, Dipartimento di Matematica - Universita degli Studi di Milano - Via C.

Saldini 50 20133 MILANO- Italy

F. Sakai, Department of Mathematics - Faculty of Science - Saitama University -

Shimo-Okubo 255, URA W A 338 - Japan. E-mail address: FSAKAI @

RIMATH. SAITAMA-U.AC.JP

G. K. Sankaran, DPMMS 16- Mill Lane- CAMBRIDGE CB2 lSB- England. E-

mail address: GKSl@ PHX.CAM.AC.UK

M. Schneider, Mathematisches lnstitut- Universitiit Bayreuth- Universitiitsstr. 30,

Postf. 10 12 51 - 8580 BAYREUTH - Germany. E-mail address: MICHAEL.SCHNEIDER@ UNI-BA YREUTH.DE

E. Sernesi, Dipartimento di Matematica - Universita degli Studi di Roma III - Via

Corrado Segre 2 - 00146 ROMA - Italy. E-mail address: SERNESI @ ITCASPUR.BITNET

F. Serrano, Departament Algebra I Geometria- Universitat DE BARCELONA-

Gran Via 585 - 08007 BARCELONA - Spain. E-mail address: UBAAGX06 @

EBCESCAl

N. Shepherd-Barron, Department of Mathematics - University of Cambridge - 16

Mill Lane - CAMBRIDGE CB 2 IS B -England N.I.SHEPHERD-BARRON

@ PMMS.CAM. AC.UK

X VIii LIST OF PARTICIPANTS

H. Sterk, Faculteit der Wiskunde en Informatica - Universiteit van Amsterdam -

Plantage Muidergracht 24- 1018 TV AMSTERDAM- The Netherlands. E-

mail address: STERK@ FWI.UV A.NL

P. Supino, Dipartimento di Matematica - Dottorato di Ricerca - Universita degli

Studi di Roma I - Piazzale Aldo Moro 5 - 00185 ROMA - Italy. E-mail

address: SUPINO@ VAXRMA.INFN.IT

Sir P. Swinnerton-Dyer, The Dower House- Thriplow- Royston- HERTS SG8

7RJ - England

G. van der Geer, Matematisch Instituut- Universiteit van Amsterdam - Plantage

Muidergracht 24- NL 1018 TV AMSTERDAM- The Netherlands. E-mail

address: GEER@ FWI.UV A.NL

A. Verra, Dipartimento di Matematica- Universita degli Studi di Roma I- Piazzale

Aldo Moro 5 - 00185 ROMA -Italy.

H. Verrill, Department Mathematics of Cambridge 16- Mill Lane- CAMBRIDGE

CB2 ISB - England

M. Teicher, Department of Mathematics- BAR-ILAN University- Bamat- Gan-

Israel. E-mail address: TEICHER @ BIMACS

J. Wahl, Department of Mathematics- University of North Carolina- Chapel Hill-

NC 27599-3250- U.S.A. E-mail address: JW@ MATH.UNC.EDU

P.M.H. Wilson, Trinity College Cambridge - CB2 ITQ - England. E-mail address:

pmhW@ pmms.cam.ac.uk

J.A. Wisniewski, Institute of Mathematics - Warsaw University - Banacha 2 - 02-

097 W ARSZA W A- Poland. E-mail address: JAREKW@ PLEARN.BITNET

F.L. Zak, CEMI RAN - Krasikov st. 32, Moscow 117418, RUSSIA. E-mail

address: Zak@ cemi.msk.su Cl0201@ sucemi

R. Zollo, Dipartimento di Matematica - Universita degli Studi di L'Aquila - Via

Vetoio Loc. Coppito- 67100 L'AQUILA- Italy

F. Zucconi, Dipartimento di Matematica - Universita degli Studi di Pisa - Via

Buonarroti 2- 56127 PISA- Italy

List of seminars held during the conference

Marco Andreatta : Elementary contractions whose supporting divisors are Kx®L®r

Enrique Arrondo : Obstructions for embedding surfaces in codimension two

Lucian B adescu : Formal functions along zero loci of sections of ample vector

bundles and applications

Fabio Bardelli : Algebraic cycles on certain Calabi-Y au threefolds

Ingrid Bauer : Generic lemniscates of algebraic functions

Stefan Bauer : Moduli of bundles on elliptic surfaces

Gian Mario Besana : On the geometry of conic bundles arising in adjunction

theory

Giorgio Bolondi : Hilbert schemes of surfaces in p4- Liaison classes of surfaces in p4

Frederic Campana : The class 'C is not stable by small deformations

Alessio Corti : Birational models for threefolds fibered in del Pezzo surfaces

Igor Dolgachev : Ogg-Shafarevich theory of elliptic threefolds

Lawrence Ein : Some Reider-type theorem for smooth threefolds

Geir Ellingsrud : Twisted cubics on a general quintic threefold

Barbara Fantecbi : Deformations of Hilbert schemes of points of a surface Hubert Flenner : Rational surfaces in 3-folds with ample normal bundle

Lothar Gottsche : Hilbert schemes of points and formulas for contacts with linear

subspaces and trisecants

Klaus Hulek : New irregular surfaces in p4

Paltin Ionescu : Roundedness for some special families of embedded manifolds

V assilii Iskovskih : Relations among generators in 2-dimensional Cremona group

over a non-closed field

Krzysztof Jaczewski: Generalized Euler Sequence and Toric Varieties

Yujiro Kawamata: On the log flips and applications

Steven L. Kleiman : A generalized Teissier-Pliicker formula

Janos Kollar : Effective base point freeness

xix

XX LIST OF SEMINARS

Kazushiro Konno : Even canonical surfaces with small K2

Angelo Lopez : Noether-Lefschetz, space curves and mathematical instantons

Marco Manetti : Deformation equivalence of surfaces

Nicolae Manolache : Multiple structures on smooth support

Rick Miranda : Encoding number for torsion sections of elliptic surfaces

Yoichi Miyaoka : Rational curves of small degree on a Fano manifold

Boris Moishezon: Cuspidal Curves and Algebraic Surfaces

Jacob Murre : Motives and Chow groups

Kieran O'Grady : On the smooth classification of projective surfaces

Christian Okonek : On the topology of non-Kiihlerian surfaces

Giorgio Ottaviani : On the relatives of the Horrocks bundle on p5

Marino Palleschi : Double covers of pn as very ample divisors

Claudio Pedrini : 0-cycles on singular projective surfaces

Thomas Peternell : Manifolds with semi-positive curvature

Ragni Piene : Projective surfaces with small osculating spaces

Giampietro Pirola : Projections on abelian variety and applications

Miles Reid : Inductive Mori theory and applications

Igor Reider : On the Chern numbers and number of moduli of surfaces of general

type

Fumio Sakai : Remarks on the irregularity of cyclic multiple planes

Michael Schneider: Bounds for stable bundles and Weierstrass schemes

Edoardo Sernesi : Torelli type theorems

Nicholas Shepherd-Barron : Some foliations on tori

Sir Peter Swinnerton-Dyer : Diophantine problems on rational varieties

Gerard van der Geer: Reed-Muller Codes and Supersingular Curves

Alessandro Verra : Prym varieties of plane sextics

Jonathan Wahl : The Miyaoka-Yau inequality for normal surfaces and local

analogues

Peltan M.H. Wilson : Calabi-Yau three folds

Jarek Wisniewski: On Fano manifolds of dimension~ 4

Fyodor Zak : Quadratic normality and higher secant varieties

Recent Titles in This Series (Continued from the front of this publication)

131 L. A. Bokut', Yu. L. Ershov, and A. I. Kostrikin, Editors, Proceedings of the International Conference on Algebra Dedicated to the Memory of A. I. Mal'cev, Parts 1, 2, and 3, 1992

130 L. Fuchs, K. R. Goodearl, J. T. Stafford, and C. Vinsonhaler, Editors, Abelian groups and noncommutative rings, 1992

129 John R. Graef and Jack K. Hale, Editors, Oscillation and dynamics in delay equations, 1992

128 Ridgley Lange and Shengwang Wang, New approaches in spectral decomposition, 1992 127 Vladimir Oliker and Andrejs Treibergs, Editors, Geometry and nonlinear partial

differential equations, 1992 126 R. Keith Dennis, Claudio Pedrini, and Michael R. Stein, Editors, Algebraic K-theory,

commutative algebra, and algebraic geometry, 1992 125 F. Thomas Bruss, Thomas S. FeJ'IUSOD, and Stephen M. Samuels, Editors, Strategies for

sequential search and selection in real time, 1992 124 Darren Haile and James Osterburg, Editors, Azumaya algebras, actions, and modules,

1992 123 Steven L. Kleiman and Anders Thorup, Editors, Enumerative algebraic geometry, 1991 122 D. H. Sattinger, C. A. Tracy, and S. Venakides, Editors, Inverse scattering and

applications, 1991 121 Alex J. Feingold, Igor B. Frenkel, and John F. X. Ries, Spinor construction of vertex

operator algebras, triality, and E~ 1 >, 1991 120 RobertS. Doran, Editor, Selfadjoint and nonselfadjoint operator algebras and operator

theory, 1991 119 Robert A. Melter, Azriel Rosenfeld, and Prabir Bhattacharya, Editors, Vision geometry,

1991 118 Yan Shi-Jian, Wang Jiagang, and Yang Chong-chon, Editors, Probability theory and its

applications in China, 1991 117 Morton Brown, Editor, Continuum theory and dynamical systems, 1991 116 Brian Harbourue and Robert Speiser, Editors, Algebraic geometry: Sundance 1988, 1991 115 Nancy Flournoy and Robert K. Tsutakawa, Editors, Statistical multiple integration, 1991 114 Jeffrey C. Laprias and Michael J. Todd, Editors, Mathematical developments arising

from linear programming, 1990 113 Eric Grinberg and Eric Todd Quinto, Editors, Integral geometry and tomography, 1990 112 Philip J. Brown and Wayne A. FuUer, Editors, Statistical analysis of measurement error

models and applications, 1990 111 Earl S. Kramer and Spyros S. Magliveras, Editors, Finite geometries and combinatorial

designs, 1990 110 Georgia Benkart and J. Marshall Osborn, Editors, Lie algebras and related topics, 1990 109 Benjamin Fine, Anthony Gaglione, and Francis C. Y. Tang, Editors, Combinatorial group

theory, 1990 108 Melvyn S. Berger, Editor, Mathematics of nonlinear science, 1990 107 Mario Milman and Tomas Schonbek, Editors, Harmonic analysis and partial differential

equations, 1990 106 Wilfried Sieg, Editor, Logic and computation, 1990 105 Jerome Kaminker, Editor, Geometric and topological invariants of elliptic operators,

1990 104 Michael Makkai and Robert Pare, Accessible categories: The foundations of categorical

model theory, 1989

(See the AMS catalog for earlier titles)

Classification of Algebraic Varieties Ciro Ciliberto, E. Laura Livorni, and Andrew J. Sommese, Editors

This volume contains the proceedings of the Algebraic Geometry Confer-ence on Classification of Algebraic Varieties, held in May 1992 at the Univer-sity of L'Aquila in Italy. The papers discuss a wide variety of problems that illustrate interactions between algebraic geometry and other branches of math-ematics. Among the topics covered are algebraic curve theory, algebraic surface theory, the theory of minimal models, braid groups and the topology of alge-braic varieties, toric varieties, Calabi-Yau three-folds, enumerative formulas, and generalizations of Kahler differential geometry. In addition to algebraic geometers, theoretical physicists in some areas will find this book useful. The book is also suitable for an advanced graduate course in algebraic geometry, as it provides an overview of some areas of current research.

ISBN 0-8218-5179-9

9 780821 851791