Equivariant stable sheaves and toric GIT
Fibrés stables équivariants et GIT torique
Résumé
For (X, L) a polarized toric variety and G ⊂ 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 gener-icity 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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