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

A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.

Christopher D. Hacon (Edited by), Mircea Musta?? (Edited by), Mihnea Popa (Edited by)

9781107647558, Cambridge University Press

Paperback / softback, published 15 January 2015

447 pages, 12 b/w illus. 9 tables
23 x 15.3 x 2.5 cm, 0.66 kg

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.

List of contributors
Preface
1. The effect of points fattening in dimension three Thomas Bauer and Tomasz Szemberg
2. Some remarks on surface moduli and determinants Aaron Bertram
3. Valuation spaces and multiplier ideals on singular varieties Sébastien Boucksom, Tommaso de Fernex, Charles Favre and Stefano Urbinati
4. Line arrangements modeling curves of high degree Gregory Burnham, Zvi Rosen, Jessica Sidmana and Peter Vermeire
5. Rationally connected manifolds and semipositivity of the Ricci curvature Frédéric Campana, Jean-Pierre Demailly and Thomas Peternell
6. Subcanonical graded rings which are not Cohen Macaulay Fabrizio Catanese
7. Threefold divisorial contractions to singularities of cE type Jungkai Alfred Chen
8. Special prime Fano fourfolds of degree 10 and index 2 Olivier Debarre, Atanas Iliev and Laurent Manivel
9. Configuration spaces of complex and real spheres Igor Dolgachev and Benjamin Howard
10. Twenty points in P3 David Eisenbud, Robin Hartshorne and Frank-Olaf Schreyer
11. The Betti table of a high degree curve is asymptotically pure Daniel Erman
12. Partial positivity: geometry and cohomology of q-ample line bundles Daniel Greb and Alex Küronya
13. Generic vanishing fails for singular varieties and in characteristic p>0 Christopher D. Hacon and Sándor J. Kovács
14. Deformations of elliptic Calabi–Yau manifolds János Kollár
15. Derived equivalence and non-vanishing loci II Luigi Lombardi and Mihnea Popa
16. The automorphism groups of Enriques surfaces covered by symmetric quartic surfaces Shigeru Mukai and Hisanori Ohashi
17. Lower order asymptotics of Szegö and Toeplitz kernels under Hamiltonian circle actions Roberto Paoletti
18. Gaussian maps and generic vanishing I: subvarieties of abelian varieties Giuseppe Pareschi
19. Torsion points on cohomology support loci: from D-modules to Simpson's theorem Christian Schnell
20. Rational equivalence of 0-cycles on K3 surfaces and conjectures of Huybrechts and O'Grady Claire Voisin.

Subject Areas: Algebraic geometry [PBMW], Mathematics [PB], Mathematics & science [P]