Cambridge University Press, 3/19/2012EAN 9780521768252, ISBN10: 052176825XHardcover, 438 pages, 23.4 x 15.6 x 2.4 cmLanguage: EnglishAlgebraic 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 Eisenbud2. Introduction to birational anabelian geometry Fedor Bogomolov and Yuri Tschinkel3. Periods and moduli Olivier Debarre4. The Hodge theory of character varieties Mark Andrea A. de Cataldo5. Rigidity properties of Fano varieties Tommaso de Fernex and Christopher D. Hacon6. The Schottky problem Samuel Grushevsky7. Interpolation Joe Harris8. Chow groups and derived categories of K3 surfaces Daniel Huybrechts9. Geometry of varieties of minimal rational tangents Jun-Muk Hwang10. Quotients by finite equivalence relations János Kollár11. Higher-dimensional analogues of K3 surfaces Kieran G. O'Grady12. Compactifications of moduli of abelian varietiesan introduction Martin Olsson13. The geography of irregular surfaces Margarida Mendes Lopes and Rita Pardini14. Basic results on irregular varieties via Fourier–Mukai methods Giuseppe Pareschi15. Algebraic surfaces and hyperbolic geometry Burt Totaro.
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