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 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 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 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