2011 Fiscal Year Final Research Report
Analytic torsion and geometry of moduli spaces
| Project/Area Number |
19340016
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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 (2010-2011)
The University of Tokyo (2007-2009) |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
ASHIKAGA Tadashi 東北学院大学, 工学部, 教授 (90125203)
KAWAGUCHI Shu 京都大学, 大学院・理学研究科, 准教授 (20324600)
KONNDO Shigeyuki 名古屋大学, 大学院・多元数理科学研究科, 教授 (50186847)
NAMIKAWA Yoshinori 京都大学, 大学院・理学研究科, 教授 (80228080)
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| Project Period (FY) |
2007 – 2011
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| Keywords | 複素解析幾何 |
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| Research Abstract |
We studied the BCOV invariant of Calabi-Yau threefolds and we determined its explicit formula in some important cases. One of our major progresses is the determination of the BCOV invariant of quantic mirror threefolds, which verified some part of the conjecture of Bershadsky-Cecotti-Ooguri-Vafa. Another major progress is the computation of the BCOV invariant of Borcea-Voisin threefolds of exceptional type, which verified the conjecture of Harvey-Moore in these cases. To obtain these results, we studied the behavior of Quillen metrics for degenerating families of varieties. In particular, we determined the singularity of Quillen metrics for one-parameter degenerating families.
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