1991 Fiscal Year Final Research Report Summary
THEORY OF ALGEBRAIC VARIETIES AND APPLICATIONS TO RELATED TOPICS
| Project/Area Number |
01540066
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | RIKKYO UNIVERSITY (1991)
Tokyo Metropolitan University (1989-1990) |
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Principal Investigator |
MIYAOKA Yoichi DEPT. MATH., RIKKYO UNIV., PROF., 理学部, 教授 (50101077)
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| Co-Investigator(Kenkyū-buntansha) |
SHIODA Tetuji DEPT. MATH, RIKKYO UNIV., PROF, 理学部, 教授 (00011627)
AOKI Noboru DEPT. MATH., RIKKYO UNIV., LECTURER, 理学部, 講師 (30183130)
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| Project Period (FY) |
1989 – 1991
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| Keywords | Fano manifolds / maximal rationally connected fibration / projective spaces and hyperquadrics / relative deformation / curves on a surface / Fermat curves / Mardell-Weil lattices / sphere packing |
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| Research Abstract |
Miyaoka (head investigator) primarily investigated rational curves on Varieties of higher dimension. Main results are as follows: (1) Construction and applications of maximal rationally connected fibrations ; (2) Study of the properties of rationally connected varieties, including geometric characterization of rationally connected 3-folds ;
(3) Proof of the rational connectedness and boundedness of Fano n-folds ;
(4) Theory of relative deformation of morphisms and application to the direct images of relative anti-canonical division as ;
Numerical charactcrizations of projective spaces and hyperguadrics ;
Proof of the boundedness of carves of given genees on a fixed surface of * type.
Decisive results to the above topics were given.
Aoki studied Fermat curves and abelian L-functions.
Shioda established the theory of Mordell-Weil lattices, to get extraordinarily rich applications such as the construction of elliptic, carves of high rank, equations with Galois group isomorphic to the Weyl groups, and a discovery of sphere packings with high density.
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