Toric sheaves and flipsArticle
Auteurs : Andrew Clarke 1; Achim Napame 2; Carl Tipler 3
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Andrew Clarke;Achim Napame;Carl Tipler
20 pages, 1 figure
[en]
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.
Volume : Volume 9
Publié le : 23 avril 2025
Accepté le : 24 septembre 2024
Soumis le : 25 octobre 2023
Mots-clés : [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], [en] Toric flips, Equivariant sheaves, Slope-stability
Financement :
Source : HAL- Interactions Brésil-France en théorie de jauge, structures extrémales et stabilité; Financeur: French National Research Agency (ANR); Code: ANR-21-CE40-0017
- Monge-Ampère réel et géométrie Kählérienne des espaces homogènes; Financeur: French National Research Agency (ANR); Code: ANR-21-CE40-0011