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

Abstract

We show that the stability conditions on the Kuznetsov component of a Gushel-Mukai threefold, constructed by Bayer, Lahoz, Macrì 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.

arXiv comment30 pages, 6 figures, final version to appear in Mathematische Nachrichten