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 $\mathsf{Ku}(X)$, 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 $\mathsf{Ku}(X)$. We also investigate the stability of acyclic extensions of non-minimal instantons.

21 pages. To appear in Journal of the Mathematical Society of Japan

References in corpus (5)

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Cited by in corpus (3)

• A note on the Kuznetsov component of the Veronese double cone
• Serre-invariant stability conditions and Ulrich bundles on cubic threefolds
• Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture