2010 Fiscal Year Final Research Report
Applications of formal loop spaces and arc spaces
| Project/Area Number |
19740016
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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 |
Algebra
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| Research Institution | Hiroshima University |
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Principal Investigator |
TAKAHASHI Nobuyoshi Hiroshima University, 大学院・理学研究科, 助教 (60301298)
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| Project Period (FY) |
2007 – 2010
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| Keywords | モティーフ的ゼータ函数 / 弦理論的不変量 / 相対Gromov-Witten不変量 |
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| Research Abstract |
I studied techniques and problems in algebraic geometry which are related to string theory, such as formal loop spaces and arc spaces. First, I obtained certain results on rationality of motivic zeta functions, which are certain functions obtained from the symmetric powers of varieties. An invariant, called nonstandard point counting, was introduced here. The structure of the totality of a string-theoretic variant of this invariant was studied. Also, I studied the contribution of a reducible curve to the relative Gromov-Witten invariant.
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