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arxiv: 2101.00138 · v2 · pith:NQNIWE2Hnew · submitted 2021-01-01 · 🧮 math.AG

Divisors computing minimal log discrepancies on lc surfaces

classification 🧮 math.AG
keywords computingminimaldiscrepancydivisorcomponentdiscrepanciesdivisorsexists
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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 $X\ni x$.

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