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Equivariant stable sheaves and toric GIT
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 153 / Issue 2 / April 2023
- Published online by Cambridge University Press:
- 07 January 2022, pp. 385-416
- Print publication:
- April 2023
-
- Article
- Export citation
-
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 $(X,\,L)$
.
