On the topological Brauer group of generalized Kummer varieties

TL;DR

This paper investigates the topological Brauer group of generalized Kummer varieties, revealing its vanishing in certain dimensions and torsion properties in others, advancing understanding of their topological invariants.

Contribution

It provides new results on the torsion and vanishing properties of the topological Brauer group for generalized Kummer varieties across different dimensions.

Findings

Brauer group vanishes when dimension is divisible by 4

Brauer group is at most 8-torsion in all other dimensions except 10

Advances understanding of topological invariants of Kummer varieties

Abstract

We study the topological Brauer group of generalized Kummer varieties. We prove that it vanishes when their dimension is divisible by 4, while for all other dimensions except dimension 10 we prove that it is at most 8-torsion.