THEORY OF ALGEBRAIC VARIETIES AND APPLICATIONS TO RELATED TOPICS

代数簇理论及其相关主题的应用

• 批准号: 01540066
• 负责人: MIYAOKA Yoichi
• 金额: $ 1.41万
• 依托单位: RIKKYO UNIVERSITY (1991)Tokyo Metropolitan University (1989-1990)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1989
• 资助国家: 日本
• 起止时间: 1989 至 1991
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-01540066/
• 关键词: 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; Mordel

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.

Miyaoka（首席研究员）主要研究高维变量上的有理曲线。主要结果如下：（1）极大有理连通纤维化的构造与应用;（2）有理连通簇的性质研究，包括有理连通3-折叠的几何刻画;（3）有理连通性与Fano n-折叠有界性的证明;（4）态射的相对变形理论及其在相对反正则除的直接象中的应用;射影空间和超二次曲面的数值特征Aoki研究了Fermat曲线和Abel L-函数，Shioda建立了Mordell-Weil格理论，得到了非常丰富的应用，如构造椭圆形，高秩的刻，Galois群同构于Weyl群的方程，高密度球填充的发现。

项目成果

T.Shioda: "Mordell-Weil latlices and sphere packings" Amer. J. Math. 113. 779-834 (1991)

T.Shioda：“Mordell-Weil 格子和球填料”Amer。

J.Koll′ar Y.Miyaoka S.Mori: "Rationally connected varieties" J.Algebraic Geomctry. 1. 429-448 (1992)

J.Koll′ar Y.Miyaoka S.Mori：“有理连通簇”J.Algebraic Geomctry。1. 429-448 (1992)

T.shioda: "Construction of elliptic curves with high rank via the invariants of the Weyl groups" J.Math.Soc.Japan. 43. 140-168 (1991)

T.shioda：“通过 Weyl 群的不变量构建高阶椭圆曲线”J.Math.Soc.Japan。

Y.miyaoka: "Multiplicative Hecke operators and applications" (in preparation).

Y.miyaoka：“乘法 Hecke 算子及其应用”（准备中）。

J.Kollar Y.Miyaoka S.Mori: "Rationally connected varieties" J. Algebraic Geometry.1. 429-448 (1992)

J.Kollar Y.Miyaoka S.Mori：“有理连通簇”J.代数几何.1。