A class of singularity of arbitrary pairs and log canonicalizations

2018/04/17 by Hashizume, Kenta · 1 citation
#14E30 #14J17 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.06326

Abstract

We define a class of singularity on arbitrary pairs of a normal variety and an effective ℝ-divisor on it, which we call pseudo-lc in this paper. This is a generalization of the usual lc singularity of pairs and log canonical singularity of normal varieties introduced by de Fernex and Hacon. By giving examples of pseudo-lc pairs which are not lc or log canonical in the sense of de Fernex--Hacon's paper, we show that pseudo-lc singularity is a strictly extended notion of those singularities. We prove that pseudo-lc pairs admit a small lc modification. We also discuss a criterion of log canonicity.

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