The minimal model program for b-log canonical divisors and applications

Daniel Chan, Kenneth Chan, Louis de Thanhoffer de Völcsey, Colin Ingalls, Kelly Jabbusch, Sándor J Kovács, Rajesh Kulkarni, Boris Lerner, Basil Nanayakkara, Shinnosuke Okawa, Michel Van den Berg

Published 2017-07-04Version 1

We discuss the minimal model program for b-log varieties, which is a pair of a variety and a b-divisor, as a natural generalization of the minimal model program for ordinary log varieties. We show that the main theorems of the log MMP work in the setting of the b-log MMP. If we assume that the log MMP terminates, then so does the b- log MMP. Furthermore, the b-log MMP includes both the log MMP and the equivariant MMP as special cases. There are various interesting b-log varieties arising from different objects, including the Brauer pairs, or "non-commutative algebraic varieties which are finite over their centres". The case of toric Brauer pairs is discussed in further detail.