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A family of categories of log terminal pairs and automorphisms of surfaces. (English) Zbl 1219.14016
Izv. Math. 74, No. 3, 541-593 (2010); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 74, No. 3, 103-156 (2010).
Any automorphism of a quasi-projective surface can be viewed as a birational transformation of a projective compactification and thus decomposes into blow-ups and blow-downs. It can moreover be viewed as a composition of elementary links between “good” compactifications, as it was done by V. I. Danilov and M. H. Gizatullin [Izv. Akad. Nauk SSSR, Ser. Mat. 39, 533–565 (1975; Zbl 0311.14002); ibid. 41, 54–103 (1977; Zbl 0357.14003)].
In the article under review, the author tries to continue their work, using singular (log terminal) compactifications instead of smooth ones. The work is done using techniques of log Mori theory and categories.

14E07 Birational automorphisms, Cremona group and generalizations
14R20 Group actions on affine varieties
14E30 Minimal model program (Mori theory, extremal rays)
14J50 Automorphisms of surfaces and higher-dimensional varieties
18A32 Factorization systems, substructures, quotient structures, congruences, amalgams
14E05 Rational and birational maps
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