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arXiv · 1804.06326

A class of singularity of arbitrary pairs and log canonicalizations

Kenta Hashizume
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Abstract

We define a class of singularity on arbitrary pairs of a normal variety and an effective $\mathbb{R}$-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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Kenta Hashizume. 2018-04-17. A class of singularity of arbitrary pairs and log canonicalizations. https://arxiv.org/abs/1804.06326

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