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arXiv · 2011.00926

Limiting mixed Hodge structures on the relative log de Rham cohomology groups of a projective semistable log smooth degeneration

Taro Fujisawa
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Abstract

We prove that the relative log de Rham cohomology groups of a projective semistable log smooth degeneration admit a natural \textit{limiting} mixed Hodge structure. More precisely, we construct a family of increasing filtrations and a family of nilpotent endomorphisms on the relative log de Rham cohomology groups and show that they satisfy a part of good properties of a nilpotnet orbit in several variables.

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Taro Fujisawa. 2020-11-02. Limiting mixed Hodge structures on the relative log de Rham cohomology groups of a projective semistable log smooth degeneration. https://arxiv.org/abs/2011.00926

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