2013 Fiscal Year Final Research Report
Mordell-Weil lattices of elliptic K3 surfaces
| Project/Area Number |
23540028
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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 | Chuo University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | K3曲面 / 楕円曲面 |
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| Research Abstract |
A K3 surface can have many different elliptic fibrations. Our objective is to classify all elliptic fibrations on a given K3 surface, and describe their Mordell-Weil lattices explicitly. Our principal result was the explicit description of the generators of the Mordell-Weil group of the elliptic fibration of rank 16 to 18 obtained from the Inose fibration on a Kummer surface of product type. This result was made possible through a series of discussions with Prof. Abhinav Kumar of MIT held in the U.S. and Japan during the period between 2012 and 2013.
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