Current Developments in Algebraic Geometry

Erscheinungsjahr 2014
ISBN: 978-1-107-45946-5
Verlag: Cambridge University Press

Buch, Englisch, Band 59, 438 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 661 g

Reihe: Mathematical Sciences Research Institute Publications

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.

Autoren/Hrsg.

Caporaso, Lucia

McKernan, James

Mustata, Mircea

Popa, Mihnea

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

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.

Über Autor(innen)

Popa, Mihnea
Mihnea Popa is a Professor of Mathematics at the University of Illinois, Chicago.

McKernan, James
James McKernan is the Norbert Wiener Professor of Mathematics at the Massachusetts Institute of Technology.

Mustata, Mircea
Mircea Mustata is a Professor of Mathematics at the University of Michigan, Ann Arbor.

Caporaso, Lucia
Lucia Caporaso is a Professor of Mathematics at the Universitá Roma Tre in Italy.