Proceedings of the Japan Academy, Series A, Mathematical Sciences

On abundance theorem for semi log canonical threefolds

Osamu Fujino

Full-text: Open access


Let $(X, \Delta)$ be a proper semi log canonical threefold with $K_X + \Delta$ nef. Then $K_X + \Delta$ is semi-ample.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 75, Number 6 (1999), 80-84.

First available in Project Euclid: 23 May 2006

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Abundance Theorem


Fujino, Osamu. On abundance theorem for semi log canonical threefolds. Proc. Japan Acad. Ser. A Math. Sci. 75 (1999), no. 6, 80--84. doi:10.3792/pjaa.75.80.

Export citation


  • F. Ambro: The locus of log canonical singularities. (1998) (preprint).
  • A. Beauville: Complex Algebraic Surfaces, 2nd ed. London Math. Soc. Stud. Texts, 34 (1996).
  • O. Fujino: Abundance theorem for semi log canonical threefolds. RIMS-1213 (1998) (preprint).
  • O. Fujino: Base point free theorem of Reid-Fukuda type (1999) (preprint).
  • T. Fujita: Fractionally logarithmic canonical rings of surfaces. J. Fac. Sci. Univ. Tokyo. 30, 685–696 (1984).
  • S. Iitaka: Algebraic Geometry, An Introduction to Birational Geometry of Algebraic Varieties. Grad. Texts in Math., 76, Springer (1981).
  • K. Karu: Minimal models and boundedness of stable varieties. preliminary version (1998) (preprint).
  • Y. Kawamata: Pluricanonical systems on minimal algebraic varieties. Inv. Math., 79, 567–588 (1985).
  • Y. Kawamata: Abundance theorem for minimal threefolds. Inv. Math., 108, 229–246 (1992).
  • Y. Kawamata: On Fujita's freeness conjecture for 3-folds and 4-folds. Math. Ann., 308, 491–505 (1997).
  • 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).
  • S. Keel, K. Matsuki, and J. McKernan: Log abundance theorem for threefolds. Duke Math. J., 75, 99–119 (1994).
  • J. Kollár: Projectivity of complete moduli. J. Differential Geom., 32, 235–268 (1990).
  • J. Kollár et al.: Flips and Abundance for Algebraic Threefolds. Astérisque, 211, Soc. Math. France (1992).
  • J. Kollár and S. Mori: Birational geometry of algebraic varieties. Cambridge Tracts in Math., 134 (1998).
  • J. Kollár and N. Shepherd-Barron: Threefolds and deformations of surface singularities. Invent. Math., 91, 299–338 (1988).
  • D. Mumford: Abelian Varieties. Oxford Univ. Press, pp. 1–242 (1970).
  • F. Sakai: Kodaira dimensions of complements of divisors, in Complex Analysis and Algebraic Geometry. Iwanami and Cambridge Univ. Press, pp. 239–257 (1977).
  • 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).
  • E. Szabó: Divisorial log terminal singularities. J. Math. Sci. Univ. Tokyo, 1, 631–639 (1995).
  • K. Ueno: Classification Theory of Algebraic Varieties and Compact Complex Spaces. Springer Lecture Notes, vol. 439, pp. 1–278 (1975).