Divisors computing minimal log discrepancies on lc surfaces

Jihao Liu; Lingyao Xie

Divisors computing minimal log discrepancies on lc surfaces

Algebraic Geometry 2021-01-21 v2

Authors: Jihao Liu , Lingyao Xie

Abstract

Let $(X\ni x,B)$ be an lc surface germ. If $X\ni x$ is klt, we show that there exists a divisor computing the minimal log discrepancy of $(X\ni x,B)$ that is a Koll\'ar component of $X\ni x$ . If $B\not=0$ or $X\ni x$ is not Du Val, we show that any divisor computing the minimal log discrepancy of $(X\ni x,B)$ is a potential lc place of $X\ni x$ .

Keywords

log canonical geometry

Cite

@article{arxiv.2101.00138,
  title  = {Divisors computing minimal log discrepancies on lc surfaces},
  author = {Jihao Liu and Lingyao Xie},
  journal= {arXiv preprint arXiv:2101.00138},
  year   = {2021}
}

Comments

19 pages. Add an example thanks to Ziquan Zhuang. Comments are welcome

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