Stability conditions on Kuznetsov components of Gushel-Mukai threefolds and Serre functor

TL;DR

This paper proves that stability conditions on Kuznetsov components of Gushel-Mukai threefolds are preserved by the Serre functor, and constructs stability conditions for related fourfolds, advancing understanding of derived categories in algebraic geometry.

Contribution

It demonstrates the invariance of stability conditions under the Serre functor for specific threefolds and extends these conditions to certain fourfolds, providing new tools for derived category analysis.

Findings

Stability conditions are preserved by the Serre functor up to a universal cover action.

Constructed stability conditions on Kuznetsov components of special Gushel-Mukai fourfolds.

Enhanced the understanding of derived categories of Gushel-Mukai varieties.

Abstract

We show that the stability conditions on the Kuznetsov component of a Gushel-Mukai threefold, constructed by Bayer, Lahoz, Macr\`i and Stellari, are preserved by the Serre functor, up to the action of the universal cover of $\text{GL}^+_2(\mathbb{R})$. As application, we construct stability conditions on the Kuznetsov component of special Gushel-Mukai fourfolds.