Nagoya Mathematical Journal

Algebraic fiber spaces whose general fibers are of maximal Albanese dimension

Osamu Fujino

Full-text: Open access

Abstract

The main purpose of this paper is to prove the Iitaka conjecture $C_{n, m}$ on the assumption that the sufficiently general fibers have maximal Albanese dimension.

Article information

Source
Nagoya Math. J., Volume 172 (2003), 111-127.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631958

Mathematical Reviews number (MathSciNet)
MR2019522

Zentralblatt MATH identifier
1084.14035

Subjects
Primary: 14D06: Fibrations, degenerations
Secondary: 14J10: Families, moduli, classification: algebraic theory

Citation

Fujino, Osamu. Algebraic fiber spaces whose general fibers are of maximal Albanese dimension. Nagoya Math. J. 172 (2003), 111--127. https://projecteuclid.org/euclid.nmj/1114631958


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References

  • J. A. Chen and C. D. Hacon, On algebraic fiber spaces over varieties of maximal Albanese dimension , Duke Math. J., 111 (2002, no. 1), 159–175.
  • O. Fujino, A canonical bundle formula for certain algebraic fiber spaces and its applications , Nagoya Math. J., 172 (2003), 129–171.
  • O. Fujino, Remarks on algebraic fiber spaces , preprint (2002).
  • O. Fujino and S. Mori, A canonical bundle formula , J. Differential Geom., 56 (2000, no. 1), 167–188.
  • C. D. Hacon and R. Pardini, On the birational geometry of varieties of maximal Albanese dimension , J. Reine Angew. Math., 546 (2002), 177–199.
  • S. Iitaka, Genera and classification of algebraic varieties. 1 , Sûgaku, 24 (1972), 14–27, (Japanese).
  • S. Iitaka, Birational Geometry for Open varieties, Les Presses de l'Université de Montréal (1981).
  • Y. Kawamata, Characterization of abelian varieties , Compositio Math., 43 (1981, no. 2), 253–276.
  • Y. Kawamata, Kodaira dimension of certain algebraic fiber spaces , J. Fac. Sci. Univ. Tokyo Sect\.IA Math., 30 (1983, no. 1), 1–24.
  • Y. Kawamata, Minimal models and the Kodaira dimension of algebraic fiber spaces , J. Reine Angew. Math., 363 (1985), 1–46.
  • J. Kollár, Subadditivity of the Kodaira dimension: fibers of general type , Algebraic geometry, Sendai, 1985, 361–398, Adv. Stud. Pure Math., 10, North-Holland, Amsterdam, 1987.
  • S. Mori, Classification of higher-dimensional varieties , Proc. Symp. Pure Math., 46 (1987), 269–331.
  • D. Mumford, Abelian varieties, Oxford Univ. Press, Oxford (1970).
  • K. Ueno, Classification Theory of Algebraic Varieties and Compact Complex Spaces, Springer Lecture Notes Vol. 439 (1975).
  • K. Ueno, On algebraic fibre spaces of abelian varieties , Math. Ann., 237 (1978, no. 1), 1–22.
  • E. Viehweg, Weak positivity and the additivity of the Kodaira dimension for certain fibre spaces , Algebraic varieties and analytic varieties (Tokyo, 1981), 329–353, Adv. Stud. Pure Math., 1, North-Holland, Amsterdam-New York, 1983.
  • E. Viehweg, Weak positivity and the stability of certain Hilbert points , Invent. Math., 96 (1989, no. 3), 639–667.