Log terminal orders are numerically rational

Details Log terminal orders are numerically rational Log terminal orders are numerically rational

2009-11-30

arxiv.org/abs/0911.5545v1

Mathematics

Algebraic Geometry

22 pages

Scientific paper

Noncommutative surfaces finite over their centres can be realised as orders over surfaces. The aim of this paper is to present a noncommutative generalisation of rational singularities, which we call numerical rationality, for such orders. We show that numerical rationality is independent of the choice of resolution. Our main result is that the log terminal orders arising from the noncommutative minimal model program, in particular, canonical orders are numerically rational. Both of these generalise well known facts about rational singularities in commutative algebraic geometry.

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