Terminal Resolutions of Brauer Pairs

TL;DR

This paper proves that for any Brauer pair, there exists a birational transformation leading to a terminal pair with positive Brauer discrepancy, thus establishing the existence of terminal resolutions for Brauer pairs.

Contribution

It introduces the concept of terminal pairs in the context of Brauer pairs and proves that every Brauer pair admits a terminal resolution through birational morphisms.

Findings

Existence of terminal pairs for any Brauer pair.

Construction of terminal resolutions via birational morphisms.

Positive Brauer discrepancy achieved in the terminal pair.

Abstract

A Brauer pair is a pair (X, {\alpha}) where X is a quasi-projective variety over an algebraically closed field and {\alpha} is an element in the 2-torsion part of the Brauer group of the function field of X. A Brauer pair (Y, {\alpha}) is a terminal pair if the Brauer discrepancy of (Y, {\alpha}) is positive. We show that given a Brauer pair (X, {\alpha}), there is a terminal pair (Y, {\alpha}) with a birational morphism Y -> X. In short, any Brauer pair admits a terminal resolution.