Topological Methods in Algebraic Transformation Groups: Proceedings of a Conference at Rutgers University (Progress in Mathematics, 80)

In recent years, there has been increasing interest and activity in the area of group actions on affine and projective algebraic varieties. TechƯ 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, algeƯ 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 asƯ 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 Content: Front Matter....Pages i-vii Introduction....Pages 1-4 Linearizing Flat Families of Reductive Group Representations....Pages 5-10 Spherical Varieties an Introduction....Pages 11-26 Homology Planes an Announcement and Survey....Pages 27-48 Fixed Point Free Algebraic Actions on Varieties Diffeomorphic to R n ....Pages 49-80 Algebraic Automorphisms of Affine Space....Pages 81-105 Almost Homogeneous Artin-Moi� ezon Varieties Under the Action of PSL2(C)....Pages 107-115 On the Topology of Curves in Complex Surfaces....Pages 117-133 The Topology of Algebraic Quotients....Pages 135-151 Rationality of Moduli Spaces via Invariant Theory....Pages 153-164 Unipotent Actions on Affine Space....Pages 165-176 Algebraic Characterization of the Affine Plane and the Affine 3-Space....Pages 177-190 Classification of Three-Dimensional Homogeneous Complex Manifolds....Pages 191-210