Semi-stable locus of a group compactification
Xuhua He, Jason Starr
TL;DR
This paper investigates the semi-stable locus in the wonderful compactification of a semisimple group, showing it is a union of stable pieces and calculating the geometric quotient, advancing understanding of group actions on compactifications.
Contribution
It identifies the semi-stable locus as a union of G-stable pieces and provides a method to compute the geometric quotient in this context.
Findings
Semi-stable locus is a union of G-stable pieces.
Explicit calculation of the geometric quotient.
Enhanced understanding of group actions on compactifications.
Abstract
In this paper, we consider the diagonal action of a connected semisimple group of adjoint type on its wonderful compactification. We show that the semi-stable locus is a union of the -stable pieces and we calculate the geometric quotient.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology · Finite Group Theory Research