Tohoku Mathematical Journal
2008
March
SECOND SERIES VOL. 60, NO. 1

Tohoku Math. J.
60 (2008), 71-100

Title MIXED HODGE STRUCTURES ON LOG SMOOTH DEGENERATIONS

Author Taro Fujisawa

(Received June 23, 2006, revised June 27, 2007)
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.

2000 Mathematics Subject Classification. Primary 14C30; Secondary 14D07, 32G20, 32S35.

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