2013 Fiscal Year Final Research Report
Degeneration of log Hodge-de Rham spectral sequences and mixed Hodge structures
| Project/Area Number |
23540058
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 東京電機大学, 工学部, 教授 (60280385)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 混合ホッジ構造 / 対数幾何学 |
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| Research Abstract |
By using cubical method, I constructed mixed Hodge structures and their polarizations on the relative log de Rham cohomology groups of a projective log deformation.
On the other hand, I considerd a projective semistable morphism over a polydisc, which is a typical example of log smooth degeneration. I proved that the limiting mixed Hodge structures give us an admissible variation of mixed Hodge structures, when the pure Hodge structures on the relative de Rham cohomology groups of general fibers degenerate to an intersection of some of coordinate hyperplanes of the polydisc.
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