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

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 GL2+(R)$\text{GL}^+_2(\operatorname{\mathbb {R}})$. As application, we construct stability conditions on the Kuznetsov component of special Gushel–Mukai fourfolds. [ABSTRACT FROM AUTHOR]