Article Dans Une Revue Épijournal de Géométrie Algébrique Année : 2023

Toric sheaves and flips

Résumé

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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Dates et versions

hal-04255427 , version 1 (24-10-2023)
hal-04255427 , version 2 (27-06-2024)
hal-04255427 , version 3 (20-04-2025)

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Andrew Clarke, Achim Napame, Carl Tipler. Toric sheaves and flips. Épijournal de Géométrie Algébrique, In press, Volume 9 (2025) (Article no. 8), ⟨10.46298/epiga.2024.12468⟩. ⟨hal-04255427v3⟩
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