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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:

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

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