Recent Advances in Algebraic Geometry

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.

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.