Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pseudo-quotients of algebraic actions and their application to character
  varieties   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.

12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics