# Divisors computing the minimal log discrepancy on a smooth surface

@article{Kawakita2017DivisorsCT, title={Divisors computing the minimal log discrepancy on a smooth surface}, author={Masayuki Kawakita}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, year={2017}, volume={163}, pages={187 - 192} }

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 computing the minimal log discrepancy computes no log canonical thresholds.

## 7 Citations

On divisors computing MLD's and LCT's

- Mathematics, Computer Science
- 2016

It is shown that if a Divisor centered over a point on a smooth surface computes a minimal log discrepancy, then the divisor also computes an asymptotic log canonical threshold of the graded sequence of ideals associated to a divisors over a variety.

On equivalent conjectures for minimal log discrepancies on smooth threefolds

- MathematicsJournal of Algebraic Geometry
- 2020

On smooth varieties, the ACC for minimal log discrepancies is equivalent to the boundedness of the log discrepancy of some divisor which computes the minimal log discrepancy. In dimension three, we…

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…

The minimal log discrepancies on a smooth surface in positive characteristic

- MathematicsMathematische Zeitschrift
- 2020

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…

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…

Shokurov's conjecture on conic bundles with canonical singularities

- Mathematics
- 2021

A conic bundle is a contraction X → Z between normal varieties of relative dimension 1 such that −KX is relatively ample. We prove a conjecture of Shokurov which predicts that, if X → Z is a conic…

ACC for local volumes and boundedness of singularities

- Mathematics
- 2020

The ACC conjecture for local volumes predicts that the set of local volumes of klt singularities $x\in (X,\Delta)$ satisfies the ACC if the coefficients of $\Delta$ belong to a DCC set. In this…

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