A refined Derived Torelli Theorem for Enriques surfaces

Abstract

We prove that two general Enriques surfaces defined over an algebraically closed field of characteristic different from $2$ are isomorphic if their Kuznetsov components are equivalent. We apply the same techniques to give a new simple proof of a conjecture by Ingalls and Kuznetsov relating the derived categories of the blow-up of general Artin\textendash Mumford quartic double solids and of the associated Enriques surfaces. This paper originated from one of the problem sections at the workshop \emph{Semiorthogonal decompositions, stability conditions and sheaves of categories}, Université de Toulouse, May 2--5, 2018.

arXiv comment30 pages. Final version to appear in Math. Ann

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Cited by in corpus (2)

• Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
• Frobenius and spherical codomains and neighbourhoods