## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Some remarks on log surfaces

Haidong Liu

#### Abstract

Fujino and Tanaka established the minimal model theory for $\mathbf{Q}$-factorial log surfaces in characteristic 0 and $p$, respectively. We prove that every intermediate surface has only log terminal singularities if we run the minimal model program starting with a pair consisting of a smooth surface and a boundary $\mathbf{R}$-divisor. We further show that such a property does not hold if the initial surface is singular.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 93, Number 10 (2017), 115-119.

Dates
First available in Project Euclid: 30 November 2017

https://projecteuclid.org/euclid.pja/1512032604

Digital Object Identifier
doi:10.3792/pjaa.93.115

Mathematical Reviews number (MathSciNet)
MR3732900

Zentralblatt MATH identifier
06850985

Subjects
Primary: 14E05: Rational and birational maps
Secondary: 14E30: Minimal model program (Mori theory, extremal rays)

#### Citation

Liu, Haidong. Some remarks on log surfaces. Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 10, 115--119. doi:10.3792/pjaa.93.115. https://projecteuclid.org/euclid.pja/1512032604

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