Recent Advances in Algebraic Geometry

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

Christopher D. Hacon, Mihnea Popa, Mircea Mustaţă

• Publisher: Cambridge University Press
• Year: 2015
• Print ISBN:
  9781107647558
• eBook ISBN:
  9781316192085
• Topic: Mathematics
• Subtopic: Topology
• Index: Mathematics

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.

Table of contents

• Cover
• Series page
• Title page
• Copyright page
• Contents
• List of contributors
• Preface
• 1 The effect of points fattening in dimension three
• 2 Some remarks on surface moduli and determinants
• 3 Valuation spaces and multiplier ideals on singular varieties
• 4 Line arrangements modeling curves of high degree: Equations, syzygies, and secants
• 5 Rationally connected manifolds and semipositivity of the Ricci curvature
• 6 Subcanonical graded rings which are not Cohen–Macaulay
• 7 Threefold divisorial contractions to singularities of cE type
• 8 Special prime Fano fourfolds of degree 10 and index 2
• 9 Configuration spaces of complex and real spheres
• 10 Twenty points in P[sup(3)]
• 11 The Betti table of a high-degree curve is asymptotically pure
• 12 Partial positivity: Geometry and cohomology of q-ample line bundles
• 13 Generic vanishing fails for singular varieties and incharacteristic p>0
• 14 Deformations of elliptic Calabi–Yau manifolds
• 15 Derived equivalence and non-vanishing loci II
• 16 The automorphism groups of Enriques surfaces covered by symmetric quartic surfaces
• 17 Lower-order asymptotics for Szegö and Toeplitz kernels under Hamiltonian circle actions
• 18 Gaussian maps and generic vanishing I: Subvarieties of abelian varieties
• 19 Torsion points on cohomology support loci: From D-modules to Simpson's theorem
• 20 Rational equivalence of 0-cycles on K3 surfaces and conjectures of Huybrechts and O'Grady