Bridgeland stability of minimal instanton bundles on Fano threefolds

2021/05/30 by Xuqiang Qin, Qin, Xuqiang
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2105.14617

openalex publication_date 2021/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that minimal instanton bundles on a Fano threefold X of Picard rank one and index two are semistable objects in the Kuznetsov component Ku(X), with respect to the stability conditions constructed by Bayer, Lahoz, Macrì and Stellari. When the degree of X is at least 3, we show torsion free generalizations of minimal instantons are also semistable objects. As a result, we describe the moduli space of semistable objects with same numerical classes as minimal instantons in Ku(X). We also investigate the stability of acyclic extensions of non-minimal instantons.

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