| 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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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,760,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥660,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000)
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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 / モチーフ的測度 / Neron-Severi格子 / Gromov-Witten不変量 / モティーフ的ゼータ関数 / モティーフ的測度 / ループ空間 / モチーフ的ゼータ函数 / モノイダル圏 / minimal log discrepangcy / ル-プ空間 / ア-ク空間 / モティ-フ的ゼータ / 代数幾何学 |
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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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