Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When does the zero fiber of the moment map have rational singularities?   Let $G$ be a complex reductive group and $V$ a $G$-module. There is a natural
moment mapping $\mu\colon V\oplus V^*\to\mathfrak{g}^*$ and we denote
$\mu^{-1}(0)$ (the shell) by $N_V$. We find criteria for $N_V$ to have rational
singularities and for the categorical quotient $N_V/\!\!/ G$ to have symplectic
singularities, the latter results improving upon [HSS20]. It turns out that for
"most" $G$-modules $V$, the shell $N_V$ has rational singularities. For the
case of direct sums of classical representations of the classical groups, $N_V$
has rational singularities and $N_V/\!\!/ G$ has symplectic singularities if
$N_V$ is a reduced and irreducible complete intersection. Another important
special case is $V=p\,\mathfrak{g}$ (the direct sum of $p$ copies of the Lie
algebra of $G$) where $p\geq 2$. We show that $N_V$ has rational singularities
and that $N_V/\!\!/ G$ has symplectic singularities, improving upon results of
[Bud19], [AA16], [Kap19] and [GH20]. Let $\pi=\pi_1(\Sigma)$ where $\Sigma$ is
a closed Riemann surface of genus $p\geq 2$. Let $G$ be semisimple and let
$\operatorname{Hom}(\pi,G)$ and $\mathscr X\!(\pi,G)$ be the corresponding
representation variety and character variety. We show that
$\operatorname{Hom}(\pi,G)$ is a complete intersection with rational
singularities and that $\mathscr X\!(\pi,G)$ has symplectic singularities. If
$p>2$ or $G$ contains no simple factor of rank $1$, then the singularities of
$\operatorname{Hom}(\pi,G)$ and $\mathscr X\!(\pi,G)$ are in codimension at
least four and $\operatorname{Hom}(\pi,G)$ is locally factorial. If, in
addition, $G$ is simply connected, then $\mathscr X\!(\pi,G)$ is locally
factorial.

17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph