Categorical Torelli theorems for Gushel-Mukai threefolds

Abstract

We show that a general ordinary Gushel-Mukai(GM) threefold $X$ is reconstructed from the Kuznetsov component $\mathcal{K}u(X)$ together with an extra data coming from tautological sub-bundle of Grassmannian $\mathrm{Gr}(2,5)$. We also prove that $\mathcal{K}u(X)$ determines birational isomorphism class of $X$, while $\mathcal{K}u(X^{\prime })$ determines the isomorphism class of a general special GM threefold $X^{\prime }$. As an application, we prove a conjecture of Kuznetsov-Perry in dimension three under a mild assumption. Finally, we use $\mathcal{K}u(X)$ to restate a conjecture of Debarre-Iliev-Manivel regarding fibers of the period map for ordinary GM threefolds.

39 pages, final version, to appear in Journal of the London Mathematical Society

References in corpus (3)

• Some remarks on Fano threefolds of index two and stability conditions
• A note on the Kuznetsov component of the Veronese double cone
• Serre-invariant stability conditions and Ulrich bundles on cubic threefolds

Cited by in corpus (1)

• On two families of Enriques categories over K3 surfaces