CONTEMPORARY MATHEMATICS

448

Algebra/ Geometry and Their Interactions

International Conference Midwest Algebra, Geometry and Their Interactions

October 7-11, 2005 University of Notre Dame, Notre Dame, Indiana

Alberto Corso Juan Migliore Claudia Polini

Editors

CoNTEMPORARY MATHEMATICS

448

Algebra, Geometry and Their Interactions

International Conference Midwest Algebra, Geometry and Their Interactions

October 7-11, 2005 University of Notre Dame, Notre Dame, Indiana

Alberto Corso Juan Migliore Claudia Polini

Editors

American Mathematical Society Providence, Rhode Island

http://dx.doi.org/10.1090/conm/448

Editorial Board Dennis DeThrck, managing editor

George Andrews Andreas Blass Abel Klein

2000 Mathematics Subject Classification. Primary 05C90, 13C40, 13D02, 13D07, 13D40, 14C05, 14J60, 14M12, 14N05, 65H10, 65H20.

Library of Congress Cataloging-in-Publication Data International Conference on Midwest Algebra, Geometry and their Interactions, MAGIC'05 (2005 : University of Notre Dame)

Algebra, geometry and their interactions : International Conference on Midwest Algebra, Geometry and their Interactions: MAGIC'05. October 7-11, 2005, University of Notre Dame, Notre Dame, Indiana/ Albert Corso, Juan Migliore, Claudia Polini, editors.

p. em. -(Contemporary mathematics, ISSN 0271-4132; v. 448) Includes bibliographical references. ISBN 978-0-8218-4094-8 (alk. paper) 1. Algebra-Congresses. 2. Geometry-Congresses. I. Corso, Alberto. II. Migliore, Juan C.

(Juan Carlos), 1956- Ill. Polini, Claudia, 1966- IV. Title.

QA150.1566 2007 512-dc22 2007060846

Copying and reprinting. Material in this book may be reproduced by any means for edu-cational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledg-ment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Acquisitions Department, American Math-ematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can also be made by e-mail to reprint-permissioniDams. org.

Excluded from these provisions is material in articles for which the author holds copyright. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.)

© 2007 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights

except those granted to the United States Government. Copyright of individual articles may revert to the public domain 28 years

after publication. Contact the AMS for copyright status of individual articles. Printed in the United States of America.

<§ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability.

Visit the AMS home page at http://www.ams.org/

10 9 8 7 6 5 4 3 2 1 12 11 10 09 08 07

Contents

Preface v

List of Talks at MAGIC'05 vii

Instability of projective reconstruction from 1-view near critical configurations in higher dimensions

MARINA BERTOLINI, GIAN MARIO BESANA, and CRISTINA TURRINI 1

Examples and counterexamples on the conjectured Hilbert function of multiple points

KAREN A. CHANDLER 13

Projectively full ideals in Noetherian rings, a survey CATALIN CIUPERCA, WILLIAM HEINZER, JACK RATLIFF, and DAVID RusH 33

Cohomological degrees and the HomAB conjecture KIA DALILI and WOLMER V. VASCONCELOS 43

A minimal generating set for the first syzygies of a monomial ideal JOHN A. EAGON 63

Lifting the determinantal property ELISA GORLA 69

Resolutions of square-free monomial ideals via facet ideals: A survey Huv TAr HA and ADAM VANTUYL 91

Some finiteness properties of Lyubeznik's F-modules MELVIN HOCHSTER 119

Minimal homogeneous liaison and licci ideals CRAIG HUNEKE, JUAN MIGLIORE, UWE NAGEL, and BERND ULRICH 129

Unobstructedness and dimension of families of codimension 3 ACM algebras JAN 0. KLEPPE and ROSA M. MIRO-ROIG 141

Ample vector bundles with sections vanishing on submanifolds of sectional genus three

ANTONIO LANTER! and HIDETOSHI MAEDA 165

Finding all real points of a complex curve YE Lu, DANIEL J. BATES, ANDREW J. SoMMESE, and CHARLES W. WAMPLER 183

iii

iv

On the multiplicity conjecture RosA M. MIR6-RoiG

CONTENTS

Efficiently detecting torsion points and subtori J. MAURICE ROJAS

Divisor class groups of graded hypersurfaces ANURAG K. SINGH and SANDRA SPIROFF

Irrelevant exceptional divisors for curves on a smooth surface KAREN E. SMITH and HOWARD M. THOMPSON

Variation of hyperplane sections MICHAEL A. VAN 0PSTALL and RAZVAN VELICHE

Jet schemes of determinantal varieties CORNELIA YUEN

207

215

237

245

255

261

Preface

The last few decades have seen a great deal of activity and developments in sev-eral areas at the interface of commutative algebra and algebraic geometry, both pure and applied. Exciting new results have also been achieved "borrowing" methods proper to neighboring fields such as combinatorics, homological algebra, polyhedral geometry, symbolic computation and topology. This volume - Algebra, Geometry and Their Interactions - highlights some of these beneficial interactions by gather-ing a collection of refereed research papers which encompass several of those aspects. Blowup algebras, linkage theory, Hilbert functions, divisors, vector bundles, deter-minantal varieties, (square-free) monomial ideals, multiplicities and cohomological degrees, and computer vision are some of the topics featured in the sixteen original research articles included in this volume. Two survey articles on topics of current interest also enrich the publication.

Many of the results published in this volume were presented during the confer-ence Midwest Algebra, Geometry and Their Interactions Conference (MAGIC'05), held at the University of Notre Dame, Indiana, during the period October 7-11, 2005. This conference continued a long-established tradition of commutative alge-bra and algebraic geometry conferences in the Midwest, among which we single out MAGIC'97 at the University of Notre Dame in 1997, BACH2 at the University of Kentucky in 2003 and the Lipman-Fest at Purdue University in 2004. MAGIC'05, though, was characterized by an applied component as well. Overall, more than one hundred and forty participants came together from numerous parts of the world, including Canada, France, Germany, India, Italy, Japan, Korea, Norway, Spain, Switzerland, the United States of America, and Venezuela. This certainly enhanced the breadth and scope of the conference. In addition, to increase the visibility of mathematics among the diverse population of Notre Dame students, as well as among the non-academic community, the conference was preceded by a public lec-ture on algebraic statistics for computational biology. The lecture was delivered by Professor Bernd Sturmfels of the University of California at Berkeley.

We would like to express our gratitude to the contributors of this volume for their enthusiasm in the project. The anonymous referees, who worked very closely with us, also deserve special credit for all their time spent in reading and correcting the original manuscripts: We are aware of the many demands on our time that the academic profession requires from each of us! We wish to express our heartfelt gratitude to the following institutions for their generous financial support: the Institute for Mathematics and its Applications (IMA) through its Participating Institution (PI) Program, the Mathematical Sciences Research Institute (MSRI) through its Network Conference Program, the National Science Foundation (NSF)

v

vi PREFACE

and the University of Notre Dame through the Center for Applied Mathematics, the College of Science, the Department of Mathematics, the Graduate School, the Notre Dame Chair in Applied Mathematics and the Vincent J. Duncan and Annamarie Micus Duncan Chair. Finally, we would like to express our thanks to Mrs. Judith Hygema for her endless efforts to make sure that the conference was a great success.

Alberto Corso, Juan Migliore and Claudia Polini Lexington and Notre Dame· August 1, 2007

List of Talks at MAGIC'05

Macaulay and Green's theorems for ideals containing a regular sequence length two

GIULIO CAVIGLIA, University of California at Berkeley

Regularity of powers of ideals MARC CHARDIN, Jussieu - Paris VI

Toroidalization of projective morphisms STEVEN DALE CUTKOSKY, University of Missouri at Columbia

Contact loci and valuations LAWRENCE EIN, University of Illinois at Chicago

G-biliaison of determinantal schemes ELISA GORLA, Universitat Zurich

Free resolution of square-free monomial ideals HUY T AI HA., Thlane University

Toward a numerical theory for the Betti numbers of ideals of fat points BRIAN HARBOURNE, University of Nebraska

Gorenstein liaison and ACM sheaves RoBIN HARTSHORNE, University of California at Berkeley

Projectively full ideals in Noetherian rings WILLIAM HEINZER, Purdue University

Some finiteness properties of Lyubeznik's F-modules MELVIN HOCHSTER, University of Michigan

Families of level algebras ANTHONY lARROBINO, Northeastern University

Parameter spaces of quotients of k[x0 , ••• , Xn] with fixed Hilbert function JAN 0. KLEPPE, Oslo University College, Norway

Asymptotic invariants of line bundles and convex bodies ROBERT LAZARSFELD, University of Michigan

Solving polynomial systems by the polyhedral homotopy continuation method TIEN-YIEN LI, Michigan State University

Biichi's 5-square problem JoSEPH LIPMAN, Purdue University

vii

viii LIST OF TALKS AT MAGIC'05

Quasicoherent and etale cohomological dimension of a scheme GENNADY LYUBEZNIK, University of Minnesota

Tilting sheaves on toric varieties RosA M. MIR6-RoiG, Universitat de Barcelona

Empty simplices of polytopes and graded Betti numbers UWE NAGEL, University of Kentucky

Pure and applied applications of numerical algebraic geometry CHRIS PETERSON, Colorado State University

Syzygies: Geometry, combinatorics and low complexity SoRIN POPESCU, State University of New York at Stony Brook

Extremal and algorithmic algebraic geometry J. MAURICE ROJAS, Texas A&M University

Constructing one-way trapdoor functions from simple semi-rings and semi-modules

JoACHIM RoSENTHAL, Universitiit Zurich

Contracted ideals MARIA EVELINA Rossi, Universita di Genova

Computing the higher direct image complex of coherent sheaves FRANK-OLAF ScHREYER, Universitiit des Saarlandes

Tight closure and positivity KAREN SMITH, University of Michigan

Multiplicity bounds HEMA SRINIVASAN, University of Missouri at Columbia

Tropical discriminants BERND STURMFELS, University of California at Berkeley

Linkage and Gorenstein linkage BERND ULRICH, Purdue University

Complexity of the normalization of algebras WOLMER VASCONCELOS, Rutgers University

Parallel algorithms for a numerical irreducible decomposition JAN VERSCHELDE, University of Illinois at Chicago

Affine semigroup rings that satisfy Serre's condition Rk MARIE VITULLI, University of Oregon

Fiber Products, exceptional varieties, and mechanisms CHARLES WAMPLER, General Motors Research and Development Center

Computing the multiplicity structure via duality ZHONGGANG ZENG, Northeastern Illinois University

Titles in This Series

448 Alberto Corso, Juan Migliore, and Claudia Polini, Editors, Algebra, geometry and their interactions, 2007

447 Franc;ois Germinet and Peter Hislop, Editors, Adventures in mathematical physics, 2007

446 Henri Berestycki, Michiel Bertsch, Felix E. Browder, Louis Nirenberg, Lambertus A. Peletier, and Laurent Veron, Editors, Perspectives in Nonliner Partial Differential Equations, 2007

445 Laura De Carli and Mario Milman, Editors, Interpolation Theory and Applications, 2007

444 Joseph Rosenblatt, Alexander Stokolos, and Ahmed I. Zayed, Editors, Topics in harmonic analysis and ergodic theory, 2007

443 Joseph Stephen Verducci and Xiaotong Shen, Editors, Prediction and discovery, 2007

442 Yi-Zhi Huang and Kailash C Misra, Editors, Lie algebras, vertex operator algbras and their applications, 2007

441 Louis H. Kauffman, David E. Radford, and Fernando J. 0. Souza, Editors, Hopf algebras and generalizations, 2007

440 Fernanda Botelho, Thomas Hagen, and James Jamison, Editors, Fluids and Waves, 2007

439 Donatella Danielli, Editor, Recent developments in nonlinear partial differential equations, 2007

438 Marc Burger, Michael Farber, Robert Ghrist, and Daniel Koditschek, Editors, Topology and robotics, 2007

437 Jose C. Mouriio, Joao P. Nunes, Roger Picken, and Jean-Claude Zambrini, Editors, Prospects in mathematical physics, 2007

436 Luchezar L. Avramov, Daniel Christensen, William G Dwyer, Michael A Mandell, and Brooke E Shipley, Editors, Interactions between homotopy theory and algebra, 2007

435 Krzysztof Jarosz, Editor, Function spaces, 2007 434 S. Paycha and B. Uribe, Editors, Geometric and topological methods for quantum field

theory, 2007 433 Pavel Etingof, Shlomo Gelaki, and Steven Shnider, Editors, Quantum groups, 2007 432 Dick Canery, Jane Gilman, Juha Heinoren, and Howard Masur, Editors, In the

tradition of Ahlfors-Bers, IV, 2007 431 Michael Batanin, Alexei Davydov, Michael Johnson, Stephen Lack, and Amnon

Neeman, Editors, Categories in algebra, geometry and mathematical physics, 2007 430 Idris Assani, Editor, Ergodic theory and related fields, 2007 429 Gui-Qiang Chen, Elton Hsu, and Mark Pinsky, Editors, Stochastic analysis and

partial differential equations, 2007 428 Estela A. Gavosto, Marianne K. Korten, Charles N. Moore, and Rodolfo H.

Torres, Editors, Harmonic analysis, partial differential equations, and related topics, 2007 427 Anastasios Mallios and Marina Haralampidou, Editors, Topological algebras and

applications, 2007 426 Fabio Ancona, Irena Lasiecka, Walter Littman, and Roberto Triggiani, Editors,

Control methods in PDE-dynamical systems, 2007 425 Su Gao, Steve Jackson, and Yi Zhang, Editors, Advances in Logic, 2007 424 V.I. Burenko, T. lwaniec, and S. K. Vodopyanov, Editors, Analysis and geometry

in their interaction, 2007 423 Christos A. Athanasiadis, Victor V. Batyrev, Dimitrios I. Dais, Martin Henk,

and Francisco Santos, Editors, Algebraic and geometric combinatorics, 2007

TITLES IN THIS SERIES

422 JongHae Keum and Shigeyuki Kondo, Editors, Algebraic geometry, 2007 421 Benjamin Fine, Anthony M. Gaglione, and Dennis Spellman, Editors,

Combinatorial group theory, discrete groups, and number theory, 2007 420 William Chin, James Osterburg, and Declan Quinn, Editors, Groups, rings and

algebras, 2006 419 Dinh V. Huynh, S. K. Jain, and S. R. L6pez-Permouth, Editors, Algebra and Its

applications, 2006 418 Lothar Gerritzen, Dorian Goldfeld, Martin Kreuzer, Gerhard Rosenberger,

and Vladimir Shpilrain, Editors, Algebraic methods in cryptography, 2006 417 Vadim B. Kuznetsov and Siddhartha Sahi, Editors, Jack, Hali-Littlewood and

Macdonald polynomials, 2006 416 Toshitake Kohno and Masanori Morishita, Editors, Primes and knots, 2006 415 Gregory Berkolaiko, Robert Carlson, Stephen A. Fulling, and Peter Kuchment,

Editors, Quantum graphs and their applications, 2006 414 Deguang Han, Palle E. T. Jorgensen, and David Royal Larson, Editors, Operator

theory, operator algebras, and applications, 2006 413 Georgia M. Benkart, Jens C. Jantzen, Zongzhu Lin, Daniel K. Nakano,

and Brian J. Parshall, Editors, Representations of algebraic groups, quantum groups and Lie algebras, 2006

412 Nikolai Chernov, Yulia Karpeshina, Ian W. Knowles, Roger T. Lewis, and Rudi Weikard, Editors, Recent advances in differential equations and mathematical physics, 2006

411 J. Marshall Ash and Roger L. Jones, Editors, Harmonic analysis: Calder6n-Zygmund and beyond, 2006

410 Abba Gumel, Carlos Castillo-Chavez, Ronald E. Mickens, and Dominic P. Clemence, Editors, Mathematical studies on human disease dynamics: Emerging paradigms and challenges, 2006

409 Juan Luis Vazquez, Xavier Cabre, and Jose Antonio Carrillo, Editors, Recent trends in partial differential equations, 2006

408 Habib Ammari and Hyeonbae Kang, Editors, Inverse problems, multi-scale analysis and effective medium theory, 2006

407 Alejandro Adem, Jesus Gonzalez, and Guillermo Pastor, Editors, Recent developments in algebraic topology, 2006

406 Jose A. de Ia Peiia and Raymundo Bautista, Editors, Trends in representation theory of algebras and related topics, 2006

405 Andrew Markoe and Eric Todd Quinto, Editors, Integral geometry and tomography, 2006

404 Alexander Borichev, Hakan Hedenmalm, and Kehe Zhu, Editors, Bergman spaces and related topics in complex analysis, 2006

403 Tyler J. Jarvis, Takashi Kimura, and Arkady Vaintrob, Editors, Gromov-Witten theory of spin curves and orbifolds, 2006

402 Zvi Arad, Mariagrazia Bianchi, Wolfgang Herfort, Patrizia Longobardi, Mercede Maj, and Carlo Scoppola, Editors, Ischia group theory 2004, 2006

401 Katrin Becker, Melanie Becker, Aaron Bertram, PaulS. Green, and Benjamin McKay, Editors, Snowbird lectures on string geometry, 2006

For a complete list of titles in this series, visit the AMS Bookstore at www.ams.org/bookstorej.

This volume's papers present work at the cutting edge of current research in algebraic geom-etry, commutative algebra, numerical analysis, and other related fields, with an emphasis on the breadth of these areas and the beneficial results obtained by the interactions between these fields. This collection of two survey articles and sixteen refereed research papers, written by experts in these fields, gives the reader a greater sense of some of the direc-tions in which this research is moving, as well as a better idea of how these fields interact with each other and with other applied areas. The topics include blowup algebras, linkage theory, Hilbert functions , divisors, vector bundles, deterrninantal varieties, (square-free) monomial ideals, multiplicities and cohomological degrees, and computer vision.

ISBN 978-0-8218-4094-8

9 780821 840948