Current Developments in Algebraic Geometry

This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.

Lucia Caporaso (Edited by), James McKernan (Edited by), Mircea Mustata (Edited by), Mihnea Popa (Edited by)

9780521768252, Cambridge University Press

Hardback, published 19 March 2012

438 pages
23.4 x 15.6 x 2.4 cm, 0.73 kg

Algebraic geometry is one of the most diverse fields of research in mathematics. It has had an incredible evolution over the past century, with new subfields constantly branching off and spectacular progress in certain directions, and at the same time, with many fundamental unsolved problems still to be tackled. In the spring of 2009 the first main workshop of the MSRI algebraic geometry program served as an introductory panorama of current progress in the field, addressed to both beginners and experts. This volume reflects that spirit, offering expository overviews of the state of the art in many areas of algebraic geometry. Prerequisites are kept to a minimum, making the book accessible to a broad range of mathematicians. 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.

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.

Subject Areas: Algebraic topology [PBPD], Topology [PBP], Algebraic geometry [PBMW], Geometry [PBM], Algebra [PBF]