Current developments in algebraic geometry
This volume, based on a workshop by the MSRI and addressed to both beginners and experts, offers an expository overview of the state of the art in many areas of algebraic geometry. Many chapters present approaches to long-standing open problems by means of modern techniques currently under development and contain questions and conjectures to help spur future research.
xi, 426 p. : illustrations ; 24 cm.
9780521768252, 052176825X
912934673
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.