[en] 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 piece of data coming from the tautological sub-bundle of the Grassmannian
$\mathrm{Gr}(2,5)$. We also prove that $\mathcal{K}u(X)$ determines the birational
isomorphism class of $X$, while $\mathcal{K}u(X')$ determines the isomorphism
class of a general special GM threefold $X'$. 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.
Disciplines :
Mathematics
Author, co-author :
JACOVSKIS, Augustinas ✱; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Lin, Xun ✱
Liu, Zhiyu ✱
Zhang, Shizhuo ✱
✱ These authors have contributed equally to this work.
Language :
English
Title :
Categorical Torelli theorems for Gushel-Mukai threefolds
