2012 Fiscal Year Final Research Report
Prospects for Mordell-Weil Lattices andAlgebraic Surfaces
| Project/Area Number |
20540051
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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 |
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| Project Period (FY) |
2008 – 2012
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| Keywords | 代数幾何学 / モーデル・ヴェイユ格子 / 代数曲面 / K3曲面 / ガロア表現 / 球のつめこみ / 整点 / グレブナ基底 |
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| Research Abstract |
We have studied selected topics on Mordell-Weil lattices (MWL) of elliptic surfaces: (1) K3 surfaces and sphere packing problem, (2) Existence and finiteness theorem of semi-stable extremal elliptic surfaces of any arithmetic genus, (3) Galois representations and algebraic equations arising from MWL, (4) Construction of multiplicative excellent families of elliptic surfaces with MWL of type E_6, E_7 or E_8, (5) Integral sections and Groebner basis, (6) Lines as generators of Neron-Severi group of Fermat surfaces.
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