MIXED HODGE STRUCTURES ON LOG SMOOTH DEGENERATIONS

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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 <i>reduced</i> log smooth degenerations.

Journal

  • Tohoku Mathematical Journal, Second Series

    Tohoku Mathematical Journal, Second Series 60(1), 71-100, 2008

    Tohoku University

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