Current Developments in Algebraic Geometry

Lucia Caporaso is a Professor of Mathematics at the Universitá Roma Tre in Italy. James McKernan is the Norbert Wiener Professor of Mathematics at the Massachusetts Institute of Technology. Mircea Mustaţă is a Professor of Mathematics at the University of Michigan, Ann Arbor. Mihnea Popa is a Professor of Mathematics at the University of Illinois, Chicago.

1. Fibers of projections and submodules of deformations Roya Beheshti and David Eisenbud; 2. Introduction to birational anabelian geometry Fedor Bogomolov and Yuri Tschinkel; 3. Periods and moduli Olivier Debarre; 4. The Hodge theory of character varieties Mark Andrea A. de Cataldo; 5. Rigidity properties of Fano varieties Tommaso de Fernex and Christopher D. Hacon; 6. The Schottky problem Samuel Grushevsky; 7. Interpolation Joe Harris; 8. Chow groups and derived categories of K3 surfaces Daniel Huybrechts; 9. Geometry of varieties of minimal rational tangents Jun-Muk Hwang; 10. Quotients by finite equivalence relations János Kollár; 11. Higher-dimensional analogues of K3 surfaces Kieran G. O'Grady; 12. Compactifications of moduli of abelian varieties: an introduction Martin Olsson; 13. The geography of irregular surfaces Margarida Mendes Lopes and Rita Pardini; 14. Basic results on irregular varieties via Fourier–Mukai methods Giuseppe Pareschi; 15. Algebraic surfaces and hyperbolic geometry Burt Totaro.