Enriques surfaces with trivial Brauer map and involutions on hyperkähler manifolds

Publikation: Arbeitspapier/Preprint › Preprint

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  • Fabian Reede

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OriginalspracheEnglisch
PublikationsstatusElektronisch veröffentlicht (E-Pub) - 12 Feb. 2024

Abstract

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 X¯. We relate the fixed locus of this involution to certain Picard schemes of the noncommutative pair (X,A), where A is an Azumaya algebra on X defined by the nontrivial element in the Brauer group of X.

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Enriques surfaces with trivial Brauer map and involutions on hyperkähler manifolds. / Reede, Fabian.
2024.

Publikation: Arbeitspapier/Preprint › Preprint

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abstract = " 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 $X$. ",
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