2009 Fiscal Year Final Research Report
Study on vector bundles and moduli spaces
| Project/Area Number |
19740036
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Kyoto University |
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Principal Investigator |
MOCHIZUKI Takuro Kyoto University, 数理解析研究所, 准教授 (10315971)
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| Project Period (FY) |
2007 – 2009
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| Keywords | ストークス構造 / ワイルド純ツイスターD加群 / ワイルド調和バンドル / 不確定特異点 / 強レフシェッツ定理 |
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| Research Abstract |
We studied wild harmonic bundles and algebraic holonomic D-modules. We established the correspondence between semisimple algebraic holonomic D-modules and polarizable wild pure twistor D-modules through wild harmonic bundles. As an application, we showed that semisimplicity of algebraic holonomic D-modules is preserved by push-forward. In the course of the study, we obtained fundamental theorems for algebraic meromorphic flat bundles, namely, a resolution of turning points, and a description of irregular singularity in terms of a system of Stokes filtrations.
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