Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T16:13:28.719Z Has data issue: false hasContentIssue false
  • English
  • Français

Algebraic fiber spaces whose general fibers are of maximal Albanese dimension

Published online by Cambridge University Press:  22 January 2016

Osamu Fujino
Osamu Fujino*
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku Nagoya, 464-8602, Japan, fujino@math.nagoya-u.ac.jp
*
Institute for Advanced Study, Einstein Drive Princeton, NJ 08540, USAfujino@math.ias.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Keywords

14J1014J4014K12
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 172 , 2003 , pp. 111 - 127
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

References

[CH] Chen, J. A. and Hacon, C. D., On algebraic fiber spaces over varieties of maximal Albanese dimension, Duke Math. J., 111 (2002), no. 1, 159–175.Google Scholar
[F1] Fujino, O., A canonical bundle formula for certain algebraic fiber spaces and its applications, Nagoya Math. J., 172 (2003), 129–171.Google Scholar
[F2] Fujino, O., Remarks on algebraic fiber spaces, preprint (2002).Google Scholar
[FM] Fujino, O. and Mori, S., A canonical bundle formula, J. Differential Geom., 56 (2000), no. 1, 167–188.Google Scholar
[HP] Hacon, C. D. and Pardini, R., On the birational geometry of varieties of maximal Albanese dimension, J. Reine Angew. Math., 546 (2002), 177–199.Google Scholar
[I1] Iitaka, S., Genera and classification of algebraic varieties. 1, Sûgaku, 24 (1972), 14–27, (Japanese).Google Scholar
[I2] Iitaka, S., Birational Geometry for Open varieties, Les Presses de l’Université de Montréal, 1981.Google Scholar
[Ka1] Kawamata, Y., Characterization of abelian varieties, Compositio Math., 43 (1981), no. 2, 253–276.Google Scholar
[Ka2] Kawamata, Y., Kodaira dimension of certain algebraic fiber spaces, J. Fac. Sci. Univ. Tokyo Sect.IA Math., 30 (1983), no. 1, 1–24.Google Scholar
[Ka3] Kawamata, Y., Minimal models and the Kodaira dimension of algebraic fiber spaces, J. Reine Angew. Math., 363 (1985), 1–46.Google Scholar
[Ko] Kollár, J., Subadditivity of the Kodaira dimension: fibers of general type, Algebraic geometry, Sendai, 1985, 361–398, Adv. Stud. Pure Math., 10, North-Holland, Amsterdam, 1987.Google Scholar
[Mo] Mori, S., Classification of higher-dimensional varieties, Proc. Symp. Pure Math., 46 (1987), 269–331.CrossRefGoogle Scholar
[Mu] Mumford, D., Abelian varieties, Oxford Univ. Press, Oxford, 1970.Google Scholar
[U1] Ueno, K., Classification Theory of Algebraic Varieties and Compact Complex Spaces, Springer Lecture Notes Vol. 439, 1975.Google Scholar
[U2] Ueno, K., On algebraic fibre spaces of abelian varieties, Math. Ann., 237 (1978), no. 1, 1–22.Google Scholar
[V1] Viehweg, E., 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.Google Scholar
[V2] Viehweg, E., Weak positivity and the stability of certain Hilbert points, Invent. Math., 96 (1989), no. 3, 639–667.CrossRefGoogle Scholar