Work

Toric sheaves and flips

Year: 2025

Type: article

Abstract: 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.

Source: Épijournal de Géométrie Algébrique

DOI: 10.46298/epiga.2024.12468

Authors: Andrew Clarke, Achim Napame, Carl Tipler

Institutions: Universidade Federal do Rio de Janeiro, Laboratoire de Mathématiques de Bretagne Atlantique

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

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