Recent Advances in Algebraic Geometry: A Volume in Honor of Rob Lazarsfeld’s 60th Birthday

doi:10.1017/CBO9781107416000

Contemporary research in algebraic geometry is the focus of this collection, which presents articles on modern aspects of the subject. The list of topics covered is a roll-call of some of the most important and active themes in this thriving area of mathematics: the reader will find articles on birational geometry, vanishing theorems, complex geometry and Hodge theory, free resolutions and syzygies, derived categories, invariant theory, moduli spaces, and related topics, all written by leading experts. The articles, which have an expository flavour, present an overall picture of current research in algebraic geometry, making this book essential for researchers and graduate students. This volume is the outcome of the conference Recent Advances in Algebraic Geometry, held in Ann Arbor, Michigan, to honour Rob Lazarsfeld's many contributions to the subject on the occasion of his 60th birthday.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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List of contributors
pp vii-x
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Preface
pp xi-xiv
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1 - The effect of points fattening in dimension three
pp 1-12
- By Th. Bauer, Philipps-Universität Marburg, T. Szemberg, Instytut Matematyki UP
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2 - Some remarks on surface moduli and determinants
pp 13-28
- By A. Bertram, University of Utah
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3 - Valuation spaces and multiplier ideals on singular varieties
pp 29-51
- By S. Boucksom, CNRS – de Jussieu Institut de Mathématiques, T. de Fernex, University of Utah, C. Favre, CNRS – École Polytechnique, S. Urbinati, Università degli Studi di Padova
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4 - Line arrangements modeling curves of high degree: Equations, syzygies, and secants
pp 52-70
- By G. Burnham, Bridgewater Associates, Z. Rosen, University of California at Berkeley, J. Sidman, Mount Holyoke College, P. Vermeire, Central Michigan University
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5 - Rationally connected manifolds and semipositivity of the Ricci curvature
pp 71-91
- By F. Campana, Université de Lorraine, J.-P. Demailly, Université de Grenoble I, Th. Peternell, Universität Bayreuth
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6 - Subcanonical graded rings which are not Cohen–Macaulay
pp 92-101
- By F. Catanese, Universität Bayreuth, J. Wahl, University of North Carolina at Chapel Hill
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7 - Threefold divisorial contractions to singularities of cE type
pp 102-122
- By J. A. Chen, National Taiwan University
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8 - Special prime Fano fourfolds of degree 10 and index 2
pp 123-155
- By O. Debarre, École Normale Supérieure et CNRS, A. Iliev, Seoul National University, L. Manivel, Université de Grenoble I et CNRS
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9 - Configuration spaces of complex and real spheres
pp 156-179
- By I. Dolgachev, University of Michigan, B. Howard, Institute for Defense Analysis
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10 - Twenty points in ℙ3
pp 180-199
- By D. Eisenbud, University of California, Berkeley, R. Hartshorne, University of California, Berkeley, F.-O. Schreyer, Universität des Saarlandes
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11 - The Betti table of a high-degree curve is asymptotically pure
pp 200-206
- By D. Erman, University of Wisconsin
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12 - Partial positivity: Geometry and cohomology of q-ample line bundles
pp 207-239
- By D. Greb, Ruhr-Universität Bochum, A. Küronya, Budapest University of Technology and Economics
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13 - Generic vanishing fails for singular varieties and in characteristic p > 0
pp 240-253
- By C. D. Hacon, University of Utah, S. J. Kovács, University of Washington
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14 - Deformations of elliptic Calabi–Yau manifolds
pp 254-290
- By J. Kollár, Princeton University
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15 - Derived equivalence and non-vanishing loci II
pp 291-306
- By L. Lombardi, Universität Bonn, M. Popa, Northwestern University
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16 - The automorphism groups of Enriques surfaces covered by symmetric quartic surfaces
pp 307-320
- By S. Mukai, Research Institute for Mathematical Sciences, Kyoto University, H. Ohashi, Tokyo University of Science
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17 - Lower-order asymptotics for Szegö and Toeplitz kernels under Hamiltonian circle actions
pp 321-369
- By R. Paoletti, Università degli Studi di Milano Bicocca
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18 - Gaussian maps and generic vanishing I: Subvarieties of abelian varieties
pp 370-404
- By G. Pareschi, Università di Roma
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19 - Torsion points on cohomology support loci: From D-modules to Simpson's theorem
pp 405-421
- By C. Schnell, Stony Brook University
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20 - Rational equivalence of 0-cycles on K3 surfaces and conjectures of Huybrechts and O'Grady
pp 422-436
- By C. Voisin, Centre de mathématiques Laurent Schwartz
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Recent Advances in Algebraic Geometry

A Volume in Honor of Rob Lazarsfeld’s 60th Birthday

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

List of contributors
pp vii-x

Preface
pp xi-xiv

1 - The effect of points fattening in dimension three
pp 1-12

2 - Some remarks on surface moduli and determinants
pp 13-28

3 - Valuation spaces and multiplier ideals on singular varieties
pp 29-51

4 - Line arrangements modeling curves of high degree: Equations, syzygies, and secants
pp 52-70

5 - Rationally connected manifolds and semipositivity of the Ricci curvature
pp 71-91

6 - Subcanonical graded rings which are not Cohen–Macaulay
pp 92-101

7 - Threefold divisorial contractions to singularities of cE type
pp 102-122

8 - Special prime Fano fourfolds of degree 10 and index 2
pp 123-155

9 - Configuration spaces of complex and real spheres
pp 156-179

10 - Twenty points in ℙ3
pp 180-199

11 - The Betti table of a high-degree curve is asymptotically pure
pp 200-206

12 - Partial positivity: Geometry and cohomology of q-ample line bundles
pp 207-239

13 - Generic vanishing fails for singular varieties and in characteristic p > 0
pp 240-253

14 - Deformations of elliptic Calabi–Yau manifolds
pp 254-290

15 - Derived equivalence and non-vanishing loci II
pp 291-306

16 - The automorphism groups of Enriques surfaces covered by symmetric quartic surfaces
pp 307-320

17 - Lower-order asymptotics for Szegö and Toeplitz kernels under Hamiltonian circle actions
pp 321-369

18 - Gaussian maps and generic vanishing I: Subvarieties of abelian varieties
pp 370-404

19 - Torsion points on cohomology support loci: From D-modules to Simpson's theorem
pp 405-421

20 - Rational equivalence of 0-cycles on K3 surfaces and conjectures of Huybrechts and O'Grady
pp 422-436

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Recent Advances in Algebraic Geometry

A Volume in Honor of Rob Lazarsfeld’s 60th Birthday

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Contents

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