Topological Methods in Algebraic Transformation Groups Proceedings of a Conference at Rutgers University

In recent years, there has been increasing interest and activity in the area of group actions on affine and projective algebraic varieties. Tech­ niques from various branches of mathematics have been important for this study, especially those coming from the well-developed theory of smooth compact transformation groups. It was timely to have an interdisciplinary meeting on these topics. We organized the conference "Topological Methods in Alg~braic Transformation Groups," which was held at Rutgers University, 4-8 April, 1988. Our aim was to facilitate an exchange of ideas and techniques among mathematicians studying compact smooth transformation groups, alge­ braic transformation groups and related issues in algebraic and analytic geometry. The meeting was well attended, and these Proceedings offer a larger audience the opportunity to benefit from the excellent survey and specialized talks presented. The main topics concerned various as­ pects of group actions, algebraic quotients, homogeneous spaces and their compactifications. The meeting was made possible by support from Rutgers University and the National Science Foundation. We express our deep appreciation for this support. We also thank Annette Neuen for her assistance with the technical preparation of these Proceedings.

Linearizing flat families of reductive group representations.- Spherical varieties: An introduction.- Homology planes: An announcement and survey.- Fixed point free algebraic actions on varieties diffeomorphic to Rn.- Algebraic automorphisms of affine space.- Almost homogeneous Artin-Moišezon varieties under the action of PSL2(C).- On the topology of curves in complex surfaces.- The topology of algebraic quotients.- Rationality of moduli spaces via invariant theory.- Unipotent actions on affine space.- Algebraic characterization of the affine plane and the affine 3-space.- Classification of 3-dimensional homogeneous complex manifolds.