Equivariant stable sheaves and toric GIT
For $(X,\,L)$ a polarized toric variety and $G\subset \mathrm {Aut}(X,\,L)$ a torus, denote by $Y$ the GIT quotient $X/\!\!/G$ . We define a family of fully faithful functors from the category of torus equivariant reflexive sheaves on $Y$ to the category of torus equivariant reflexive sheaves on $X$ . We show, under a genericity assumption on $G$ , that slope stability is preserved by these functors if and only if the pair $((X,\,L),\,G)$ satisfies a combinatorial criterion. As an application, when $(X,\,L)$ is a polarized toric orbifold of dimension $n$ , we relate stable equivariant reflexive sheaves on certain $(n-1)$ -dimensional weighted projective spaces to stable equivariant reflexive sheaves on $(X,\,L)$ .
Keyword(s):
2013 ◽
Vol 155
(3)
◽
pp. 517-527
Keyword(s):
2009 ◽
2020 ◽
Vol 5
(3)
◽
pp. 92-100
Keyword(s):
2017 ◽
Vol 8
(4)
◽
pp. 167