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

On the multiplicity conjecture RosA M. MIR6-RoiG 207 Efficiently detecting torsion points and subtori J. MAURICE ROJAS 215 Divisor class groups of graded hypersurfaces ANURAG K. SINGH and SANDRA SPIROFF 237 Irrelevant exceptional divisors for curves on a smooth surface KAREN E. SMITH and HOWARD M. THOMPSON 245 Variation of hyperplane sections MICHAEL A. VAN 0PSTALL and RAZVAN VELICHE 255 Jet schemes of determinantal varieties CORNELIA YUEN 261 Preface

The last few decades have seen a great deal of activity and developments in sev- eral areas at the interface of and algebraic geometry, both pure and applied. Exciting new results have also been achieved "borrowing" methods proper to neighboring fields such as combinatorics, , 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 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, 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, 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

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