| Project/Area Number |
01540066
|
|---|
| Research Category |
Grant-in-Aid for General Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
代数学・幾何学
|
|---|
| Research Institution | RIKKYO UNIVERSITY (1991)
Tokyo Metropolitan University (1989-1990) |
|---|
Principal Investigator |
MIYAOKA Yoichi DEPT. MATH., RIKKYO UNIV., PROF., 理学部, 教授 (50101077)
|
|---|
| 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)
栗原 将人 東京都立大学, 理学部, 助手 (40211221)
中島 晴久 東京都立大学, 理学部, 助教授 (90145657)
佐々井 崇雄 東京都立大学, 理学部, 助教授 (00094269)
辻 元 東京都立大学, 理学部, 助教授 (30172000)
笹倉 頌夫 東京都立大学, 理学部, 教授 (20087026)
卜部 東介 東京都立大学, 理学部, 助手 (70145655)
荻上 絋一 東京都立大学, 理学部, 教授 (10087025)
|
|---|
| Project Period (FY) |
1989 – 1991
|
| Project Status |
Completed (Fiscal Year 1991)
|
| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1991: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1990: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1989: ¥800,000 (Direct Cost: ¥800,000)
|
|---|
| Keywords | Fano manifolds / maximal rationally connected fibration / projective spaces and hyperquadrics / relative deformation / curves on a surface / Fermat curves / Mardell-Weil lattices / sphere packing / 極大有理連結部分多様体 / 極大有理連結ファイブレ-ション / 相対変形理論 / 位相型の有限性 / MordellーWeil格子 / Q上の楕円曲線 / 球体充てん / 有理連結性 / 有界性定理 / 分類理論 / Hecke作用素 / KaGG"HHhlenーEinstein計量 / 一般型多様体 / 一般Hecke作用素 / 楕円モデュラ-型式 / モデユライ理論 / 相対双対層 / 反射層 / 曲面孤立特異点 / Monoge-Ampere方程式 |
|---|
| 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.
|
