2015 Fiscal Year Final Research Report
Analytic torsion and geometry
| Project/Area Number |
23340017
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MATSUZAWA Junichi 奈良女子大学, 自然科学系, 教授 (00212217)
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| Co-Investigator(Renkei-kenkyūsha) |
KAWAGUCHI Shu 同志社大学, 大学院理工学研究科, 教授 (20324600)
NAMIKAWA Yoshinori 京都大学, 大学院理学研究科, 教授 (80228080)
MUKAI Shigeru 京都大学, 数理解析研究所, 教授 (80115641)
MORIWAKI Atsushi 京都大学, 大学院理学研究科, 教授 (70191062)
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| Project Period (FY) |
2011-04-01 – 2016-03-31
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| Keywords | 解析的捩率 / 保型形式 / モジュライ空間 / K3曲面 / Calabi-Yau多様体 / BCOV不変量 / Borcherds積 |
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| Outline of Final Research Achievements |
We studied the holomorphic torsion invariant of 2-elementary K3 surfaces and we determined its explicit formula as a function on the moduli space. It turned out that, for all topological types of involutions, the holomorphic torsion invariant is expressed as the product of an explicit Borcherds product and theta constants.
We also studied the BCOV invariant of Calabi-Yau threefolds and we determined its explicit formula as a function on the moduli space for Borcea-Voisin threefolds. We introduced BCOV invariants for Calabi-Yau orbifolds and made comparison of BCOV invariants between Borcea-Voisin orbifolds and their crepant resolution.
We studied the Borcherds Phi-function and obtained its algebraic expression. Namely, the value of the Borcherds Phi-function at the period of an Enriques surface is expressed as the product of its period and the resultant of its defining equation. As a by-product, we obtained an infinite product expression of theta constants of genus 2.
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| Free Research Field |
複素幾何学
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