Several complex variables 06: complex manifolds

The articles in this volume were written to commemorate Reinhold Remmert's 60th birthday in June, 1990. They are surveys, meant to facilitate access to some of the many aspects of the theory of complex manifolds, and demonstrate the interplay between complex analysis and many other branches of mathematics, algebraic geometry, differential topology, representations of Lie groups, and mathematical physics being only the most obvious of these branches. Each of these articles should serve not only to describe the particular circle of ideas in complex analysis with which it deals but also as a guide to the many mathematical ideas related to its theme. Some of the topics dealt with are the following: recent developments in the theory of proper holomorphic maps; the enormous influence and power of Hodge structures (and families of such structures); the mutual influence of complex analysis and representation theory in the study of (almost) homogeneous complex manifolds; the influence of ideas from mathematical physics (via the Yang-Mills equation and stable vector bundles) on the study of the topology of complex algebraic surfaces; the fruitfulness of studying spaces of compact Riemann surfaces and of compact Kähler manifolds from the point of view of the curvature of theses spaces. Thus, the present volume should provide some idea of the richness of the theory of complex manifolds. Offers an introduction and a survey of the theory of complex spaces, an important subject in the theory of several complex variables. Written by experts who have developed substantial parts of the field, this book is useful for graduates, researchers in complex analysis, algebraic and differential geometry, and also, mathematical physicists. This volume contains a series of essays which aim to facilitate access to many aspects of the theory of complex manifolds, and demonstrate the interplay between complex analysis and other branches of mathematics, algebraic geometry, differential topology and mathematical physics.