Current Topics in Complex Algebraic Geometry

by Edited by Herbert Clemens , Janos Kollár

• ISBN13: 9780521562447
• ISBN10: 0521562449
• Format: Hardcover
• Copyright: 1996-01-26
• Publisher: Cambridge University Press

Summary

The 1992/93 academic year at the Mathematical Sciences Research Institute was devoted to Complex Algebraic Geometry. This volume collects survey articles that arose from this event, which took place at a time when algebraic geometry was undergoing a major change. To put it succinctly, algebraic geometry has opened up to ideas and connections from other fields that have traditionally been far away. The editors of the volume, Herbert Clemens and János Kollár, chaired the organising committee. Activities were centred around themes, one per month, under the guidance of experts in each area. There were also four short workshops, which attracted many participants and helped considerably in communicating the new directions in algebraic geometry to a large audience. This book gives a good idea of the intellectual content of the special year and of the workshops. These articles represent very well the change of direction and branching out witnessed by algebraic geometry in the last few years.

Table of Contents

Preface	ix
Janos Kollar
Fundamental Groups of Smooth Projective Varieties	1	(16)
Donu Arapura
Vector Bundles on Curves and Generalized Theta Functions: Recent Results and Open Problems	17	(18)
Arnaud Beauville
Recent Results in Higher Dimensional Birational Geometry	35	(22)
Alessio Corti
The Schottky Problem: An Update	57	(8)
Olivier Debarre
Spectral Covers	65	(22)
Ron Donagi
Adjoint Linear Systems	87	(10)
Lawrence Ein
Torelli Groups and Geometry of Moduli Spaces of Curves	97	(48)
Richard M. Hain
Vector bundles and Brill-Noether theory	145
Shigeru Mukai