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Fujino, Osamu

On abundance theorem for semi log canonical threefolds. (English) Zbl 0990.14005

Proc. Japan Acad., Ser. A 75, No. 6, 80-84 (1999).
O. Fujino [Duke Math. J. 102, 513-532 (2000; Zbl 0986.14007)] proved an abundance theorem for semi log canonical threefolds. In the present paper he gives an exposition of his theorem. His theorem is a generalization of the log abundance theorem for threefolds shown by S. Keel, K. Matsuki and J. McKernan [Duke Math. J. 75, 99-119 (1994; Zbl 0818.14007)].
Reviewer: Aigli Papantonopoulou (Ewing)

Cited in 1 Document

MSC:

14E30 Minimal model program (Mori theory, extremal rays)
14J30 \(3\)-folds
14C20 Divisors, linear systems, invertible sheaves
14E07 Birational automorphisms, Cremona group and generalizations

Keywords:

abundance theorem; semi log canonical threefolds

Citations:

Zbl 0986.14007; Zbl 0818.14007
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\textit{O. Fujino}, Proc. Japan Acad., Ser. A 75, No. 6, 80--84 (1999; Zbl 0990.14005)
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References:

[1] F. Ambro: The locus of log canonical singularities. (1998) (preprint).
[2] A. Beauville: Complex Algebraic Surfaces, 2nd ed. London Math. Soc. Stud. Texts, 34 (1996). · Zbl 0849.14014
[3] O. Fujino: Abundance theorem for semi log canonical threefolds. RIMS- 1213 (1998) (preprint). · Zbl 0986.14007
[4] O. Fujino: Base point free theorem of Reid-Fukuda type (1999) (preprint). · Zbl 0971.14009
[5] T. Fujita: Fractionally logarithmic canonical rings of surfaces. J. Fac. Sci. Univ. Tokyo. 30 , 685-696 (1984). · Zbl 0543.14004
[6] S. Iitaka: Algebraic Geometry, An Introduction to Birational Geometry of Algebraic Varieties. Grad. Texts in Math., 76 , Springer (1981). · Zbl 0491.14005
[7] K. Karu: Minimal models and boundedness of stable varieties. preliminary version (1998) (preprint). · Zbl 0980.14008
[8] Y. Kawamata: Pluricanonical systems on minimal algebraic varieties. Inv. Math., 79 , 567-588 (1985). · Zbl 0593.14010
[9] Y. Kawamata: Abundance theorem for minimal threefolds. Inv. Math., 108 , 229-246 (1992). · Zbl 0777.14011
[10] Y. Kawamata: On Fujita’s freeness conjecture for 3-folds and 4-folds. Math. Ann., 308 , 491-505 (1997). · Zbl 0909.14001
[11] Y. Kawamata, K. Matsuda, and K. Matsuki: Introduction to the Minimal Model Problem, in Algebraic Geometry, Sendai 1985 . Adv. Stud. Pure Math., 10 , Kinokuniya and North-Holland, 283-360 (1987). · Zbl 0672.14006
[12] S. Keel, K. Matsuki, and J. McKernan: Log abundance theorem for threefolds. Duke Math. J., 75 , 99-119 (1994). · Zbl 0818.14007
[13] J. Kollár: Projectivity of complete moduli. J. Differential Geom., 32 , 235-268 (1990). · Zbl 0684.14002
[14] J. Kollár et al. : Flips and Abundance for Algebraic Threefolds. Astérisque, 211 , Soc. Math. France (1992).
[15] J. Kollár and S. Mori: Birational geometry of algebraic varieties. Cambridge Tracts in Math., 134 (1998).
[16] J. Kollár and N. Shepherd-Barron: Threefolds and deformations of surface singularities. Invent. Math., 91 , 299-338 (1988). · Zbl 0642.14008
[17] D. Mumford: Abelian Varieties. Oxford Univ. Press, pp. 1-242 (1970). · Zbl 0223.14022
[18] F. Sakai: Kodaira dimensions of complements of divisors, in Complex Analysis and Algebraic Geometry . Iwanami and Cambridge Univ. Press, pp. 239-257 (1977). · Zbl 0375.14009
[19] V. V. Shokurov: 3-fold log flips. Izv. Ross. Akad. Nauk Ser. Mat., 56 , 105-203 (1992); Russian Acad. Sci. Izv. Math. 40 , 95-202 (1993) (translated in English).
[20] E. Szabó: Divisorial log terminal singularities. J. Math. Sci. Univ. Tokyo, 1 , 631-639 (1995). · Zbl 0835.14001
[21] K. Ueno: Classification Theory of Algebraic Varieties and Compact Complex Spaces. Springer Lecture Notes, vol. 439, pp. 1-278 (1975). · Zbl 0299.14007
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