2021/08/17 by Borisov, Lev, Chan, Vernon, Wang, Chengxi
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2108.07768
Let V be a 6-dimensional complex vector space with an involution σ of trace 0, and let W ⊂ \Sym2 V^\vee be a generic 3-dimensional subspace of σ-invariant quadratic forms. To these data we can associate an Enriques surface as the σ-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.