Several Complex Variables

Several Complex Variables is a central area of mathematics with strong interactions with partial differential equations, algebraic geometry, number theory, and differential geometry. The 1995–1996 MSRI program on Several Complex Variables emphasized these interactions and concentrated on developments and problems of interest that capitalize on this interplay of ideas and techniques. This collection, first published in 2000, provides a remarkably clear and complete picture of the status of research in these overlapping areas and will provide a basis for significant continued contributions from researchers. Several of the articles are expository or have extensive expository sections, making this an excellent introduction for students to the use of techniques from these other areas in several complex variables. Thanks to its distinguished list of contributors this volume provides a representative sample of the work done in Several Complex Variables.

Preface; 1. Local holomorphic equivalence of real analytic submanifolds in CN M. Salah Baouendi and Linda Preiss Rothschild; 2. How to use cycle space in complex geometry Daniel Barlet; 3. Resolution of singularities Edward Bierstone and Pierre D. Milman; 4. Global regularity of the ?-Neuman problem: a survey of the L2-Sobolev theory Harold P. Boas and Emial J. Straube; 5. Recent developments in the classification theory of compact Käehler manifolds Frederic Campana and Thomas Peternell; 6. Remarks on global irregularity in the ?-Neumann problem Michael Christ; 7. Subelliptic estimates and finite type John P. D'Angelo and Joseph J. Kohn; 8. Pseudoconvex-concave duality and regularization of currents Jean-Pierre Demailly; 9. Complex dynamics in higher dimension John Erik Fornaess and Nessim Sibony; 10. Attractors in ?2 John Erik Fornaess and Brendan Weickert; 11. Analytic Hilbert quotients Peter Heinzner and Alan Huckleberry; 12. Varieties of minimal rational tangents on uniruled projective manifolds Jun-Muk Hwang and Ngaiming Mok; 13. Recent developments in Seiberg–Witten theory and complex geometry Christian Okonek and Andrei Teleman; 14. Recent techniques in hyperbolicity problems Yum-Tong Siu; 15. Rigidity theorems in Käehler geometry and fundamental groups of varieties Domingo Toledo; 16. Nevanlinna theory and diophantine approximation Paul Vojta.

First published in 2000, this book provides a clear and complete picture of research in Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry. The expository nature of the articles makes this an excellent introduction for students as well as a basis for continuing research.