Several Complex Variables VI : 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 many aspects of the theory of complex manifolds, and demonstrate the interplay between complex analysis and other branches of mathematics, algebraic geometry, differential topology, representations of Lie groups and mathematical physics. 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 include 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 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 Kahler manifolds from the point of view of the curvature of these spaces. Thus, the present volume should provide some idea of the richness of the theory of complex manifolds.