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Limits of Hodge Structure in Several Variables

Published online by Cambridge University Press:  04 December 2007

TARO FUJISAWA
TARO FUJISAWA
Affiliation:
Nagano National College of Technology, 716 Tokuma, Nagano 381, Japan; e-mail: fujisawa@cc.nagano-nct.ac.jp
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Abstract

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We define the notion of a morphism of generalized semi-stable type, which is a generalization of the notion of a semistable degeneration over a curve. We partially generalize Steenbrink‘s results on the limit of Hodge structures to the case of such a morphism. As an application we prove the E1-degeneration of the relative Hodge–De Rham spectral sequence for this case.

Keywords

variation of Hodge structureslimit of Hodge structureslog structuremorphism of generalized semi-stable type.
Type
Research Article
Information
Compositio Mathematica , Volume 115 , Issue 2 , February 1999 , pp. 129 - 183
Copyright
© 1999 Kluwer Academic Publishers