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, 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.