2015 Fiscal Year Final Research Report
A study on the cohomology of the moduli spaces of Riemann surfaces
| Project/Area Number |
24740028
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Tokyo Denki University |
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Principal Investigator |
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| Research Collaborator |
KONISHI Yukiko 京都大学, 大学院理学研究科, 准教授 (30505649)
BERGSTÖM Jonas ストックホルム大学
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | モジュライ空間 / コホモロジー / 混合フロベニウス構造 |
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| Outline of Final Research Achievements |
We studied moduli spaces of Riemann surfaces with marked points, with a particular emphasis on their cohomology rings. The symmetric groups act on these spaces via permutation of marked points. We determined the character of the cohomology as a representation of the symmetric groups in the genus zero case. We also studied some related moduli spaces of weighted stable curves, called Losev-Manin space and its genus one analogue. In addition to these, we made a study on the mixed Frobenius structure and local quantum cohomology.
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| Free Research Field |
代数幾何学
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