2017/07/04 by Chan, Daniel, Chan, Kenneth, de Völcsey, Louis de Thanhoffer +8
#14A22 #14E30 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1707.00834
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.