Tohoku Mathematical Journal

Mixed Hodge structures on log smooth degenerations

Taro Fujisawa

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Abstract

We introduce the notion of a log smooth degeneration, which is a logarithmic analogue of the central fiber of some kind of degenerations of complex manifolds over polydiscs. Under suitable conditions, we construct a natural cohomological mixed Hodge complex on the reduction of a compact log smooth degeneration. In particular, we obtain mixed Hodge structures on the log de Rham cohomologies and $E_1$-degeneration of the log Hodge to de Rham spectral sequence for a certain kind of compact reduced log smooth degenerations.

Article information

Source
Tohoku Math. J. (2), Volume 60, Number 1 (2008), 71-100.

Dates
First available in Project Euclid: 28 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1206734407

Digital Object Identifier
doi:10.2748/tmj/1206734407

Mathematical Reviews number (MathSciNet)
MR2419037

Zentralblatt MATH identifier
1147.14004

Subjects
Primary: 14C30: Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture
Secondary: 14D07: Variation of Hodge structures [See also 32G20] 32G20: Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30] 32S35: Mixed Hodge theory of singular varieties [See also 14C30, 14D07]

Citation

Fujisawa, Taro. Mixed Hodge structures on log smooth degenerations. Tohoku Math. J. (2) 60 (2008), no. 1, 71--100. doi:10.2748/tmj/1206734407. https://projecteuclid.org/euclid.tmj/1206734407


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