Divisors computing minimal log discrepancies on lc surfaces

preprint2021arXivOpen access

Abstract

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

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