
TL;DR
This paper investigates the structure of Luna strata in quotient spaces of rational G-modules, focusing on torsors, divisor class groups, and Cox rings, revealing reasons for their singularities.
Contribution
It introduces methods to compute divisor class groups and Cox rings of Luna strata using torsors, explaining their boundary singularities.
Findings
Computed divisor class groups of Luna strata
Determined Cox rings under mild assumptions
Identified causes of boundary singularities
Abstract
Let G be a reductive group and X be a Luna stratum on the quotient space V//G of a rational G-module V. We consider torsors over X with both non-commutative and commutative structure groups. It allows us to compute the divisor class group and the Cox ring of a Luna stratum under mild assumptions. This techniques gives a simple cause why many Luna strata are singular along their boundary.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory
