Brauer groups of singular del Pezzo surfaces

TL;DR

This paper investigates how rational singularities influence the Brauer group of surfaces and provides explicit computations for all singular del Pezzo surfaces over algebraically closed fields.

Contribution

It offers a comprehensive description of the Brauer groups of singular del Pezzo surfaces, including cases with rational singularities, which was previously not fully understood.

Findings

Computed Brauer groups for all singular del Pezzo surfaces over algebraically closed fields.

Established the relationship between rational singularities and Brauer group structure.

Provided explicit descriptions and classifications of Brauer groups in these cases.

Abstract

We describe the effect of rational singularities on the Brauer group of a surface, and compute the Brauer groups of all singular del Pezzo surfaces over an algebraically closed field.