Conics on Gushel-Mukai fourfolds, EPW sextics and Bridgeland moduli spaces

Abstract

We identify the double dual EPW sextic ${\tilde{Y}}_{A^{\perp }}$ and the double EPW sextic ${\tilde{Y}}_A$, associated with a very general Gushel-Mukai fourfold $X$, with the Bridgeland moduli spaces of stable objects of character ${\Lambda }_1$ and ${\Lambda }_2$ in the Kuznetsov component $\mathcal{K}u(X)$. This provides an affirmative answer to a question of Perry-Pertusi-Zhao. As an application, we prove a conjecture of Kuznetsov-Perry for very general Gushel-Mukai fourfolds.

27 pages, made changes according to referee's suggestions. To appear in Math. Res. Lett. Comments are welcome!