Bridgeland stability of minimal instanton bundles on Fano threefolds

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.