• Corpus ID: 230435597

Divisors computing minimal log discrepancies on lc surfaces

  title={Divisors computing minimal log discrepancies on lc surfaces},
  author={Jihao Liu and Lingyao Xie},
Let (X ∋ x,B) be an lc surface germ. If X ∋ x is klt, we show that there exists a divisor computing the minimal log discrepancy of (X ∋ x,B) that is a Kollár component of X ∋ x. If B 6= 0 or X ∋ x is not Du Val, we show that any divisor computing the minimal log discrepancy of (X ∋ x,B) is a potential lc place of X ∋ x. 
1 Citations
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Recent study in K-stability suggests that klt singularities whose local volumes are bounded away from zero should be bounded up to special degeneration. We show that this is true in dimension three,


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Abstract We study a divisor computing the minimal log discrepancy on a smooth surface. Such a divisor is obtained by a weighted blow-up. There exists an example of a pair such that any divisor
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