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.

arXiv comment21 pages. To appear in Journal of the Mathematical Society of Japan

References in corpus (12)

• Hilbert schemes of lines and conics and automorphism groups of Fano threefolds
• Instanton bundles on Fano threefolds
• Stability conditions on Kuznetsov components
• Projectivity and Birational Geometry of Bridgeland Moduli spaces on an Enriques Surface
• Stability conditions on Fano threefolds of Picard number one
• The MMP for deformations of Hilbert schemes of points on the projective plane
• The desingularization of the theta divisor of a cubic threefold as a moduli space
• Rational curves and instantons on the Fano threefold $Y_5$
• Some remarks on Fano threefolds of index two and stability conditions
• A note on the Kuznetsov component of the Veronese double cone
• Compactification of the moduli space of instanton sheaves on the Fano threefold $V_5$
• ACM bundles on cubic threefolds

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