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- Title
Pseudo-quotients of algebraic actions and their application to character varieties.
- Authors
González-Prieto, Ángel
- Abstract
In this paper, we propose a weak version of quotient for the algebraic action of a group on a variety, which we shall call a pseudo-quotient. They arise when we focus on the purely topological properties of good Geometric Invariant Theory (GIT) quotients regardless of their algebraic properties. The flexibility granted by their topological nature enables an easier identification in geometric constructions than classical GIT quotients. We obtain several results about the interplay between pseudo-quotients and good quotients. Additionally, we show that in characteristic zero pseudo-quotients are unique up to virtual class in the Grothendieck ring of algebraic varieties. As an application, we compute the virtual class of S L 2 (k) -character varieties for free groups and surface groups as well as their parabolic counterparts with punctures of Jordan type.
- Subjects
RING theory; TOPOLOGICAL property; FREE surfaces; HODGE theory
- Publication
Communications in Contemporary Mathematics, 2024, Vol 26, Issue 4, p1
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199723500098