Equivariant stable sheaves and toric GIT

Andrew Clarke; Carl Tipler

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arXiv · 2001.01500

Equivariant stable sheaves and toric GIT

Andrew Clarke·Carl Tipler

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Abstract

For (X,L) a polarized toric variety and G a torus of automorphisms of (X,L), 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 (X, L) to stable equivariant reflexive sheaves on certain (n-1)-dimensional weighted projective spaces.

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BibTeX RIS

Andrew Clarke, Carl Tipler. 2020-01-06. Equivariant stable sheaves and toric GIT. https://arxiv.org/abs/2001.01500

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