2007 Fiscal Year Final Research Report Summary
A study on mixed Hodge structures on the relative log de Rham cohomology groups of log smooth degenerations
| Project/Area Number |
18540060
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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 | Nagano National College of Technology |
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Principal Investigator |
FUJISAWA Taro Nagano National College of Technology, dep. of general education, associate prof. (60280385)
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| Project Period (FY) |
2006 – 2007
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| Keywords | mixed Hodge structure / weight filtrations / logarithmic structures |
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| Research Abstract |
In 2006, I studied the case of semi-stable degeneration of compact Kahler complex manifolds, as an important example of log smooth degenerations. In particular, weight filtrations on the mixed Hodge complexes constructed on the singular fibers were considered deeply. I found that the properties of these weight filtrations were related to the properties of monodromy logarithms
In 2007, I have been studying these weight filtrations and found that the monodromy logarithms played important roles to construct the weight filtrations for the case of log smooth degenerations.
The monodromy action on the cohomology groups is quasi-unipotent in general. However I expect that we can construct mixed Hodge complexes, for the case of log smooth degeneration, by the reduction to the case where the monodromy actions are unipotent, once I find out the appropriate conditions which assures the unipotency of the monodromy.
In order to find out such conditions, I calculated the cohomology sheaves of the relative log de Rham complexes for log smooth degenerations.
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