# The minimal log discrepancies on a smooth surface in positive characteristic

@article{Ishii2020TheML, title={The minimal log discrepancies on a smooth surface in positive characteristic}, author={Shihoko Ishii}, journal={Mathematische Zeitschrift}, year={2020}, volume={297}, pages={389-397} }

This paper shows that Mustaţǎ–Nakamura’s conjecture holds for pairs consisting of a smooth surface and a multiideal with a real exponent over the base field of positive characteristic. As corollaries, we obtain the ascending chain condition of the minimal log discrepancies and of the log canonical thresholds for those pairs. We also obtain finiteness of the set of the minimal log discrepancies of those pairs for a fixed real exponent.

## 4 Citations

A bound of the number of weighted blow-ups to compute the minimal log discrepancy for smooth 3-folds

- Mathematics
- 2021

We study a pair consisting of a smooth 3-fold defined over an algebraically closed field and a “general" real ideal. We show that the minimal log discrepancy (“mld" for short) of every such a pair is…

Divisors computing minimal log discrepancies on lc surfaces

- Mathematics
- 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…

Upper bound of discrepancies of divisors computing minimal log discrepancies on surfaces

- Mathematics
- 2020

Fix a subset $I\subseteq \mathbb R_{>0}$ such that $\gamma=\inf\{ \sum_{i}n_ib_i-1>0 \mid n_i\in \mathbb Z_{\geq 0}, b_i\in I \}>0$. We give a explicit upper bound $\ell(\gamma)\in O(1/\gamma^2)$ as…

On boundedness of divisors computing minimal log discrepancies for surfaces

- Mathematics
- 2020

Let $\Gamma$ be a finite set, and $X\ni x$ a fixed klt germ. For any lc germ $(X\ni x,B:=\sum_{i} b_iB_i)$ such that $b_i\in \Gamma$, Nakamura's conjecture, which is equivalent to the ACC conjecture…

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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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