Toric sheaves and flips
20 pages, 1 figure 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.
Authors
- Achim Napame (ORCID: https://orcid.org/0000-0003-0365-1012)
- Andrew Clarke (ORCID: https://orcid.org/0000-0001-9480-4912)
- Carl Tipler (ORCID: https://orcid.org/0000-0003-1388-7213)
Institutions
- Universidade Federal do Rio de Janeiro (BR)
- Laboratoire de Mathématiques de Bretagne Atlantique (FR)
Publication Details
- Journal
- Épijournal de Géométrie Algébrique
- Published
- 2025-04-23
- DOI
- https://doi.org/10.46298/epiga.2024.12468
- Primary Topic
- Logic, programming, and type systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Agence Nationale de la Recherche
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Universidade Federal do Rio de Janeiro