2007 Fiscal Year Final Research Report Summary
Mordell-Weil Lattices and Cycles on Algebraic Surfaces
| Project/Area Number |
17540044
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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 | Rikkyo University |
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Principal Investigator |
SHIODA Tetsuji Rikkyo University, Faculty of Sci., Professor Emeritus (00011627)
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| Co-Investigator(Kenkyū-buntansha) |
AOKI Noboru Rikkyo Univ., Faculty of Sci., Professor (30183130)
KAKEI Saburo Rikkyo Univ., Faculty of Sci., Assoc. Professor (60318798)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Mordell-Weil Lattices / K3 surfaces / Rational elliptic surfaces / Kummer surfaces / Sphere packing problem / Gauss sums / Painleve equations / ソリトン方程式 |
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| Research Abstract |
The following results have been accomplished on Algebraic cycles on K3 surfaces which forms the main theme of this research proposal :
(i) We have determined, for an example of a K3 surface attaining the maximal Mordell-Weil rank 18, the structure of its Mordell-Weil lattice, explicit generators of rational points, together with the splitting field.[2]
(ii) More generally, we have clarified the structure of the transcendental lattice, Neron-Severi lattice and the Mordell-Weil lattice, of the singular K3 surfaces which arise via the cyclic base change of degree up to six from Inose's elliptic K3 surface. Ref.[3] and in preparation, and (3).
(iii) Classical Kummer surfaces attached to genus two Jacobian varieties are studied from the viewpoint of Mordell-Weil lattices, which establishes the close relationship of automorphisms of a genus two curve with the singular fibres and generators of the Mordell-Weil lattice in question. Ref.[4].
(iv) In a joint work with M.Kuwata, we have determined the elliptic parameters and the defining equations of elliptic fibrations on the Kummer surface of the product of two non-isogenous elliptic crves., which has been classified by Oguiso by geometric method. Ref.[6].
[The rest is omitted in this English summary because of the space limitation.]
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Research Products
(40 results)
