Basil Nanayakkara | Searcharxiv

arXiv2017

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

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.

math.AG↗

arXiv2011

Terminal Resolutions of Brauer Pairs

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

math.AG↗