Fujino, Osamu Semi-stable minimal model program for varieties with trivial canonical divisor. (English) Zbl 1230.14016 Proc. Japan Acad., Ser. A 87, No. 3, 25-30 (2011). The author gives a sufficient condition for the termination of flips. By using this result a semi-stable minimal model program for varieties with (numerically) trivial canonical divisor is derived. Finally the author treats a slight refinement of dlt blow-ups. Reviewer: Anargyros Katsabekis (Lamia) Cited in 20 Documents MSC: 14E30 Minimal model program (Mori theory, extremal rays) 14D06 Fibrations, degenerations in algebraic geometry Keywords:semi-stable minimal model; varieties with trivial canonical divisor; termination of flips; movable divisors; movable cone × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] W. Barth, C. Peters and A. Van de Ven, Compact complex surfaces , Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 4, Springer, Berlin, 1984. · Zbl 0718.14023 [2] C. Birkar, On existence of log minimal models, Compos. Math. 146 (2010), no. 4, 919-928. · Zbl 1197.14011 · doi:10.1112/S0010437X09004564 [3] C. Birkar, P. Cascini, C. Hacon and J. M\(^{\text{c}}\)Kernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010), no. 2, 405-468. · Zbl 1210.14019 · doi:10.1090/S0894-0347-09-00649-3 [4] F. Campana, V. Koziarz and M. Păun, Numerical character of the effectivity of adjoint line bundles. (Preprint). · Zbl 1250.14009 [5] S. Druel, Quelques remarques sur la décomposition de Zariski divisorielle sur les variétés dont la première classe de Chern est nulle, Math. Z., (2009). (to appear). · Zbl 1216.14007 · doi:10.1007/s00209-009-0626-4 [6] O. Fujino, Abundance theorem for semi log canonical threefolds, Duke Math. J. 102 (2000), no. 3, 513-532. · Zbl 0986.14007 · doi:10.1215/S0012-7094-00-10237-2 [7] O. Fujino, On termination of 4-fold semi-stable log flips, Publ. Res. Inst. Math. Sci. 41 (2005), no. 2, 281-294. · Zbl 1102.14011 · doi:10.2977/prims/1145475354 [8] O. Fujino, Special termination and reduction to pl flips, in Flips for 3-folds and 4-folds , 63-75, Oxford Lecture Ser. Math. Appl., 35 Oxford Univ. Press, Oxford, 2007. · Zbl 1286.14025 · doi:10.1093/acprof:oso/9780198570615.003.0004 [9] O. Fujino, Fundamental theorems for the log minimal model program, arXiv: · Zbl 1234.14013 · doi:10.2977/PRIMS/50 [10] O. Fujino and S. Mori, A canonical bundle formula, J. Differential Geom. 56 (2000), no. 1, 167-188. · Zbl 1032.14014 [11] Y. Gongyo, Abundance theorem for numerical trivial log canonical divisors of semi-log canonical pairs. (Preprint). · Zbl 1312.14024 · doi:10.1090/S1056-3911-2012-00593-1 [12] Y. Gongyo, Minimal model theory of numerical Kodaira dimension zero. (Preprint). · Zbl 1246.14026 [13] Y. Kawamata, K. Matsuda and K. Matsuki, Introduction to the minimal model problem, in Algebraic geometry, Sendai, 1985 , 283-360, Adv. Stud. Pure Math., 10 North-Holland, Amsterdam. · Zbl 0672.14006 [14] J. Kollár, et al., Flips and abundance for algebraic threefolds , Soc. Math. France, Paris, 1992. [15] J. Kollár and S. Mori, Birational geometry of algebraic varieties , translated from the 1998 Japanese original, Cambridge Tracts in Mathematics, 134, Cambridge Univ. Press, Cambridge, 1998. [16] C.-J. Lai, Varieties fibered by good minimal models, arXiv: · Zbl 1221.14018 · doi:10.1007/s00208-010-0574-7 [17] Y. Miyaoka and S. Mori, A numerical criterion for uniruledness, Ann. of Math. (2) 124 (1986), no. 1, 65-69. · Zbl 0606.14030 · doi:10.2307/1971387 [18] S. Takayama, On uniruled degenerations of algebraic varieties with trivial canonical divisor, Math. Z. 259 (2008), no. 3, 487-501. · Zbl 1138.14008 · doi:10.1007/s00209-007-0235-z This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.