投影半稳定对数光滑退化的相对log-de-Ram上同调群上的极限混合Hodge结构

Pub Date : 2020-11-02 DOI:10.1215/21562261-10607345

T. Fujisawa

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引用次数: 3

摘要

我们证明了投影半稳定对数光滑退化的相对log-de-Ram上同调群承认一个自然的｛textit｛limiting｝混合Hodge结构。更确切地说，我们在相对log de Rham上同调群上构造了一个增加滤子族和一个幂零自同态族，并证明它们在几个变量中满足幂零网轨道的一部分好性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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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