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arXiv · 2309.09267

Toric sheaves and flips

Andrew Clarke·Achim Napame·Carl Tipler
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Abstract

Any toric flip naturally induces an equivalence between the associated categories of equivariant reflexive sheaves, and we investigate how slope stability behaves through this functor. On one hand, for a fixed toric sheaf, and natural polarisations that make the exceptional loci small, we provide a simple numerical criterion that characterizes when slope stability is preserved through the flip. On the other hand, for a given flip, we introduce full subcategories of logarithmic toric sheaves and characterize when polystability is preserved for all toric sheaves in those subcategories at once.

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Andrew Clarke, Achim Napame, Carl Tipler. 2023-09-17. Toric sheaves and flips. https://arxiv.org/abs/2309.09267

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