Derived Partners of Enriques Surfaces

Lev Borisov; Vernon Chan; Chengxi Wang

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arXiv · 2108.07768

Derived Partners of Enriques Surfaces

Lev Borisov·Vernon Chan·Chengxi Wang

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Abstract

Let $V$ be a $6$-dimensional complex vector space with an involution $\sigma$ of trace $0$, and let $W \subset \Sym^2 V^\vee$ be a generic $3$-dimensional subspace of $\sigma$-invariant quadratic forms. To these data we can associate an Enriques surface as the $\sigma$-quotient of the complete intersection of the quadratic forms in $W$. We exhibit noncommutative Deligne-Mumford stacks together with sheaves of Azumaya algebras on them whose derived categories are equivalent to those of the Enriques surfaces. This provides a more accessible treatment of of Theorem 6.16 in https://www.ams.org/journals/jams/2021-34-02/S0894-0347-2021-00963-3/ .. We also construct geometric realizations of the Brauer classes coming from these sheaves of Azumaya algebras which may be of independent interest.

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Lev Borisov, Vernon Chan, Chengxi Wang. 2021-08-17. Derived Partners of Enriques Surfaces. https://arxiv.org/abs/2108.07768

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