2010 Fiscal Year Final Research Report
Mixed Hodge structures on log smooth degenerations
| Project/Area Number |
20540054
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo Denki University |
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Principal Investigator |
FUJISAWA Taro Tokyo Denki University, 工学部, 准教授 (60280385)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 混合ホッジ構造 / 対数構造 |
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| Research Abstract |
I succeeded to construct "product" and "the trace map" on the relative log de Rham cohomology groups of a log deformation, which is a typical example of log smooth degeneration. Moreover, I proved that these data provided a polarization on mixed Hodge structures, where the polarization is not a bilinear form on the graded pieces by the weight filtration on the log de Rham cohomology groups, but a bilinear form on the whole log de Rham cohomology groups satisfying the appropriated properties on the graded pieces by the weight filtration.
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