Recent Advances in Algebraic Geometry A Volume in Honor of Rob Lazarsfeld’s 60th Birthday London Mathematical Society Lecture Note Series

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.

Christopher D. Hacon is a distinguished professor at the University of Utah. He is a recipient of the 2007 Clay Research Award, the 2009 Cole Prize, and the 2011 Antonio Feltrinelli Prize in Mathematics, Mechanics and Applications. He has been a Fellow of the American Mathematical Society since 2012.
Mircea Mustaţă is a professor at the University of Michigan, Ann Arbor. In addition to being a fellow of the American Mathematical Society since 2012, he was a Clay Research Fellow (2001–4) and a Packard Fellow (2006–11).
Mihnea Popa is a Professor of Mathematics at University of Illinois, Chicago. Starting in 2014, he will hold the same position at Northwestern University. He was a recipient of a Clay Liftoff Fellowship in 2001, an AMS Centennial Fellowship 2005–7, and a Sloan Fellowship 2007–9.