Mathematics > Algebraic Geometry
[Submitted on 23 Jul 2018 (v1), last revised 2 Nov 2023 (this version, v5)]
Title:Pseudo-quotients of algebraic actions and their application to character varieties
View PDFAbstract: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 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 $\mathrm{SL}_{2}(k)$-character varieties for free groups and surface groups as well as their parabolic counterparts with punctures of Jordan type.
Submission history
From: Ángel González-Prieto Dr. [view email][v1] Mon, 23 Jul 2018 11:36:52 UTC (43 KB)
[v2] Tue, 13 Nov 2018 17:37:33 UTC (34 KB)
[v3] Wed, 2 Sep 2020 21:16:24 UTC (41 KB)
[v4] Fri, 16 Apr 2021 13:38:26 UTC (51 KB)
[v5] Thu, 2 Nov 2023 00:26:43 UTC (46 KB)
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