On Brauer groups of known Enriques manifolds

TL;DR

This paper calculates the Brauer groups of certain Enriques manifolds, constructs specific Brauer-Severi varieties on them, and analyzes the pull-back map to their hyper-Kähler universal covers from geometric and algebraic viewpoints.

Contribution

It provides explicit computations of Brauer groups for known Enriques manifolds and explores the properties of associated Brauer-Severi varieties and their pull-back maps.

Findings

Brauer groups of some Enriques manifolds are explicitly computed.

Special Brauer-Severi varieties are constructed on these manifolds.

The pull-back map from the Brauer group of an Enriques manifold to its universal cover is studied.

Abstract

We compute the Brauer group of some of the known Enriques manifolds. We then build special Brauer-Severi varieties on these manifolds and study the pull-back map from the Brauer group of an Enriques manifold to that of its hyper-K\"ahler universal cover, from both a geometric and an algebraic perspective.