Compact quotients by C^∗-actions

Daniel Joseph Gross

Vol. 114 (1984), No. 1, 149–164

DOI: 10.2140/pjm.1984.114.149

Abstract

Let X be a compact normal complex space on which C^∗ acts ‘in a nice manner’. We describe all invariant open subsets U of X such that the holomorphic map U → U∕C^∗ of U onto the categorical quotient for the category of compact complex spaces, U∕C^∗, is locally Stein. The description depends on a partial ordering of the fixed point components which arises from the Bialynicki-Birula decompositions of X.

Mathematical Subject Classification 2000

Primary: 32M05

Secondary: 32C20, 32J25

Milestones

Received: 8 August 1982

Revised: 20 February 1983

Published: 1 September 1984