Current Topics in Complex Algebraic Geometry

The 1992/3 academic year at the Mathematical Sciences Research Institute was devoted to complex algebraic geometry. This 1996 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 Janos Kollar, chaired the organizing committee. Activities were centered 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. Review of the hardback: '... an overview of recent developments in the subject ... While this is inevitably a book for the expert, the contributors have tried not to become too technical.' MathematicaPreface Janos Kollar; 1. Fundamental groups of smooth projective varieties Donu Arapura; 2. Vector bundles on curves and generalized theta functions: recent results and open problems Arnaud Beauville; 3. Recent results in higher dimensional birational geometry Alessio Corti; 4. The Schottky problem: an update Olivier Debarre; 5. Spectral covers Ron Donagi; 6. Adjoint linear systems Lawrence Ein; 7. Torelli groups and geometry of moduli spaces of curves Richard M. Hain; 8. Vector bundles and Brill-Noether theory Shigeru Mukai.