Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A correspondence of good G-sets under partial geometric quotients   For a complex variety $\hat X$ with an action of a reductive group $\hat G$
and a geometric quotient $\pi: \hat X \to X$ by a closed normal subgroup $H
\subset \hat G$, we show that open sets of $X$ admitting good quotients by
$G=\hat G / H$ correspond bijectively to open sets in $\hat X$ with good $\hat
G$-quotients. We use this to compute GIT-chambers and their associated
quotients for the diagonal action of $\text{PGL}_2$ on $(\mathbb{P}^1)^n$ in
certain subcones of the $\text{PGL}_2$-effective cone via a torus action on
affine space. This allows us to represent these quotients as toric varieties
with fans determined by convex geometry.

10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph