## Some remarks on log surfaces.(English)Zbl 1388.14045

A pair $$(X, \Delta)$$ where $$X$$ is a normal algebraic surface and $$\Delta$$ is a boundary real divisor such that the adjoint bundle $$K_X+\Delta$$ is $$\mathbb{R}$$-Cartier is called a log surface. It has been proved (see the Introduction of this paper and references therein) that if $$X$$ is $$\mathbb{Q}$$-factorial the log minimal model program runs (both in characteristic $$0$$ and $$p>0$$). In the paper under review (see Theorem 1.2) it is shown that when starting with a smooth surface, every intermediate surface in the program has only log terminal singularities. Moreover, this does not hold when the initial surface is singular.

### MSC:

 1.4e+06 Rational and birational maps 1.4e+31 Minimal model program (Mori theory, extremal rays)
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### References:

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