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.


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