Quotients of complete intersections by C^∗ actions

Richard Cranston Randell

Vol. 74 (1978), No. 1, 209–219

DOI: 10.2140/pjm.1978.74.209

Abstract

We consider complete intersections V in C^m which have an isolated singularity at 0. When V admits a C^∗ action, one has the orbit space V ^∗ = V −{0}∕C^∗. In this paper we determine when V ^∗ is a topological manifold, or in some cases, the precise dimension of the set Σ along which V ^∗ is not a manifold. For proper actions we consider a naturaI complex structure on the space V ^∗ and determine some equivalences among V ^∗ for different V . Our methods are topological; the results are expressed numerically in terms of weighted degrees of the polynomials defining V .

Mathematical Subject Classification 2000

Primary: 32C40, 32C40

Secondary: 14B05

Milestones

Received: 14 February 1977

Published: 1 January 1978