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Toric sheaves and flips

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arxiv 2309.09267 v2 pith:BQUFDGS3 submitted 2023-09-17 math.AG

Andrew Clarke , Achim Napame , Carl Tipler This is my paper · ORCID
classification math.AG
keywords toricsheavesfliphandpreservedslopestabilitysubcategories
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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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  1. Polynomial stability conditions for vector bundles: Positivity, equivariance and blow-ups

    math.AG 2025-06 accept novelty 6.0 of 10

    P-critical connections generalize Z-critical connections; on toric varieties P-positivity is checked finitely, and uniform P-positivity survives point blow-ups.

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