Twisted Fourier-Mukai partners of Enriques surfaces

TL;DR

This paper proves that complex Enriques surfaces have no twisted Fourier-Mukai partners other than themselves, extending previous results to include non-trivial Brauer classes using twisted K-theory and Mukai lattices.

Contribution

It extends the uniqueness of Fourier-Mukai partners for Enriques surfaces to the twisted setting, showing no non-trivial twisted partners exist.

Findings

Twisted Fourier-Mukai partners of Enriques surfaces are trivial.

Uses twisted topological K-theory and Mukai lattices as main tools.

Confirms the uniqueness of the derived category for Enriques surfaces even with non-trivial Brauer classes.

Abstract

Bridgeland and Maciocia showed that a complex Enriques surface X has no Fourier-Mukai partners apart from itself: that is, if D^b(X) = D^b(Y) then X = Y. We extend this to twisted Fourier-Mukai partners: if alpha is the non-trivial element of Br(X) = Z/2 and D^b(X,alpha) = D^b(Y,beta), then X = Y and beta is non-trivial. Our main tools are twisted topological K-theory and twisted Mukai lattices.