2011 Fiscal Year Final Research Report
Arithmetic study of Calabi-Yau varieties with fibration
| Project/Area Number |
21540003
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Hokkaido University of Education |
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Principal Investigator |
GOTO Yasuhiro 北海道教育大学, 教育学部, 准教授 (40312425)
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| Research Collaborator |
YUI Noriko クイーンズ大学, 数理科学研究科, 教授
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| Project Period (FY) |
2009 – 2011
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| Keywords | カラビ・ヤウ多様体 / 数論幾何 / ゼータ関数 / L関数 / モジュラリティ / 形式群 |
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| Research Abstract |
We studied the arithmetic of Calabi-Yau threefolds with fibration by elliptic curves and/or K3 surfaces. The focus was put on Calabi-Yau threefolds of Delsarte type defined in a weighted projective space over a number field and also on Calabi-Yau threefolds considered by Voisin and Borcea in their construction of mirror symmetry. Taking into account the information of fibrations, we computed the cohomology, zeta functions and L-functions of such Calabi-Yau threefolds. We moreover obtained results on their modularity (automorphy) and on the height of their formal groups.
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