# Divisors computing minimal log discrepancies on lc surfaces

@inproceedings{Liu2021DivisorsCM, title={Divisors computing minimal log discrepancies on lc surfaces}, author={Jihao Liu and Lingyao Xie}, year={2021} }

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.

## One Citation

On boundedness of singularities and minimal log discrepancies of Koll\'ar components

- Mathematics
- 2022

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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