Arithmetic aspects of Calabi-Yau surfaces and the hypergeometric system
| Project/Area Number |
23540061
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Chiba University |
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Principal Investigator |
SHIGA Hironori 千葉大学, 理学(系)研究科(研究院), 名誉教授 (90009605)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Keywords | K3 曲面 / 保型形式 / 超幾何函数 / 周期写像 / アーベル曲面 / アーベル多様体 / カラビヤウ曲面 / 保型写像 / 志村多様体 / Calabi-Yau manifold / K3 surface / period map / hypergeometric function / modular form |
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| Research Abstract |
In this project we aimed to find a new aspect of the period map for the K3 surfaces based on the hypergeometric differential equations. We expected arithmetic applications of our approach also. For it, it is basic to obtain explicit representations of the modular functions those arise as the inverse of the period map. There are various foregoing studies for the moduli of abelian surfaces. But there was no exact result to describe the modular maps based on the geometric back ground. We found a good description of the
parameter space for it by considering a family of elliptic K3 surfaces those are Hodge equivalent to the family of abelian surfaces. By this idea we succeeded to solve the above problem. The main result will be published as
"Modular maps for the family of abelian surfaces via K3 surfaces", Math. Nachrichten (2014)(in printing, joint work with A. Nagano).
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Report
(4 results)
Research Products
(18 results)
