Semistability conditions defined by ample classes

2024/02/12 by Damien Mégy, Mégy, Damien, Mihai Pavel +3 · 3 citations
Computer Science · Mathematics · #14D20 #32G13 #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Equations Stability Results #Fuzzy Systems and Optimization #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2402.07758

openalex publication_date 2024/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a class of semistability conditions defined by a system of ample classes for coherent sheaves over a smooth projective variety. Under some necessary boundedness assumptions, we show the existence of a well-behaved chamber structure for the variation of moduli spaces of sheaves with respect to the change of semistability.

Cited by

• Generalized Bogomolov Inequalities
• Polynomial stability conditions for vector bundles: Positivity, equivariance and blow-ups
• Polynomial Bridgeland Stability Conditions on the Category of Coherent Sheaves

Related

• Moduli of PT-semistable objects II
• Boundedness of semistable sheaves
• Uniform boundedness of semistable pure sheaves on projective manifolds
• Slope-semistability and moduli of coherent sheaves: a survey
• On the structure of semistable rigid sheaves on algebraic surfaces