Let $X$ be an Enriques surface. Using Beauville's result about the triviality of the Brauer map of $X$, we define a new involution on the category of coherent sheaves on the canonically covering K3 surface $\overline{ X}$. We relate the fixed locus of this involution to certain Picard schemes of the noncommutative pair $(X,\mathcal{ A})$, where $\mathcal{ A}$ is an Azumaya algebra on $X$ defined by the nontrivial element in the Brauer group of $X$.
Categories: math.AG