Hostname: page-component-f7d5f74f5-qghsn Total loading time: 0 Render date: 2023-10-04T14:52:18.905Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "coreDisableSocialShare": false, "coreDisableEcommerceForArticlePurchase": false, "coreDisableEcommerceForBookPurchase": false, "coreDisableEcommerceForElementPurchase": false, "coreUseNewShare": true, "useRatesEcommerce": true } hasContentIssue false

Algebraic fiber spaces whose general fibers are of maximal Albanese dimension

Published online by Cambridge University Press:  22 January 2016

Osamu Fujino*
Graduate School of Mathematics, Nagoya University, Chikusa-ku Nagoya, 464-8602, Japan,
Institute for Advanced Study, Einstein Drive Princeton, NJ 08540,
Rights & Permissions [Opens in a new window]


Core share and HTML view are not possible as this article does not have html 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.


Research Article
Copyright © Editorial Board of Nagoya Mathematical Journal 2003


[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, 159175.Google Scholar
[F1] Fujino, O., A canonical bundle formula for certain algebraic fiber spaces and its applications, Nagoya Math. J., 172 (2003), 129171.CrossRefGoogle 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, 167188.CrossRefGoogle Scholar
[HP] Hacon, C. D. and Pardini, R., On the birational geometry of varieties of maximal Albanese dimension, J. Reine Angew. Math., 546 (2002), 177199.Google Scholar
[I1] Iitaka, S., Genera and classification of algebraic varieties. 1, Sûgaku, 24 (1972), 1427, (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, 253276.Google Scholar
[Ka2] Kawamata, Y., Kodaira dimension of certain algebraic fiber spaces, J. Fac. Sci. Univ. Tokyo Sect.IA Math., 30 (1983), no. 1, 124.Google Scholar
[Ka3] Kawamata, Y., Minimal models and the Kodaira dimension of algebraic fiber spaces, J. Reine Angew. Math., 363 (1985), 146.Google Scholar
[Ko] Kollár, J., Subadditivity of the Kodaira dimension: fibers of general type, Algebraic geometry, Sendai, 1985, 361398, 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), 269331.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, 122.CrossRefGoogle Scholar
[V1] Viehweg, E., Weak positivity and the additivity of the Kodaira dimension for certain fibre spaces, Algebraic varieties and analytic varieties (Tokyo, 1981), 329353, 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, 639667.CrossRefGoogle Scholar