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A canonical bundle formula for certain algebraic fiber spaces and its applications

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, USA, fujino@math.ias.edu
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Abstract

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We investigate period maps of polarized variations of Hodge structures of weight one or two. We treat the case when the period domains are bounded symmetric domains. We deal with a relationship between canonical extensions of some Hodge bundles and automorphic forms. As applications, we obtain a canonical bundle formula for certain algebraic fiber spaces, such as Abelian fibrations, K3 fibrations, and solve Iitaka’s famous conjecture Cn,m for some algebraic fiber spaces.

Keywords

14J1514J1014N3014J40
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 172 , 2003 , pp. 129 - 171
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

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