Log Centres of Noncommutative Crepant Resolutions are Kawamata Log Terminal: Remarks on a paper of Stafford and van den Bergh

TL;DR

This paper proves that under certain algebraic conditions, the pair of the centre and ramification divisor of a prime algebra forms a Kawamata log terminal pair, linking noncommutative resolutions with algebraic geometry.

Contribution

It establishes a new connection between noncommutative crepant resolutions and Kawamata log terminal pairs in algebraic geometry.

Findings

The pair (centre, ramification divisor) is Kawamata log terminal under specified conditions.

Provides a bridge between noncommutative algebra and algebraic geometry.

Extends understanding of singularities in noncommutative settings.

Abstract

We show that if a finitely generated prime algebra $\Delta$ is a finitely generated maximal Cohen-Macaulay module over its centre $Z$, and has global dimension equal to $\dim Z$, then the pair given by its centre and ramification divisor is Kawamata log terminal.