Synthetic research of algebraic geometry with an expectation of wide applications

代数几何的综合研究，有望得到广泛应用

• 批准号: 09304001
• 负责人: ISHIDA Masanori
• 金额: $ 21.31万
• 依托单位: TOHOKU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09304001/
• 关键词: Algebraic geometry; Algebraic variety; Toric variety; Commutative algebra; Computational geometry; Abelian variety; モジュライ空間; 組合せ論; モーデルベイユ格子; カラビヤウ多様体; グレーブナー基底; アインシュタイン計量

Ishida studied on fans which define toric varieties. He described them as schemes based on semigroups.Nakamura gave an explanation on the McKay correspondences of simple singularities. And he constructed a natural compactification of the moduli space of abelian varieties.Katsura worked on the code theory. He also got some results on hights of the formal Brauer groups defined for polarized K3 surfaces in positive characteristics.Shioda studied on the Mordell-Weil lattices of elliptic curves and Jacobian varieties.Mori gave a direct proof of the existing theorem of the semi-universal deformation space of hypersurface isolated singularities.Saito got a formula for the enumeration problem of the curves with high genera embedded in rational elliptic surfaces.Sato proved that projective varieties with some special properties spanned by rational curves is either a projective space or a quadric hypersurface.Hashimoto studied on affine schemes with actions of affine group schemes. And he applied the results for the invariant theory.Other investigators and cooperators organized The Symposium of Algebra, The Symposium of Algebraic geometry and The Symposium of Commutative Algebras. The results which we got through these symposia are published in the proceedings of these symposia.

石田研究风扇定义复曲面品种。他将它们描述为基于半群的方案。中村对简单奇点的麦凯对应进行了解释。他构造了阿贝尔簇模空间的自然紧化。桂致力于码理论。Shioda研究了椭圆曲线的Mordell-Weil格和Jacobian簇，Mori给出了半-Weil格存在定理的直接证明，Shioda研究了椭圆曲线的Mordell-Weil格和Jacobian簇，Mori给出了半-Weil格存在定理的直接证明。超曲面孤立奇点的泛变形空间，得到了有理椭圆曲面中高亏格曲线的计数公式证明了由有理曲线张成的具有某些特殊性质的射影簇是射影空间或二次超曲面，Hashimoto研究了具有仿射群作用的仿射格式。其他研究者和合作者组织了代数专题讨论会、代数几何专题讨论会和交换代数专题讨论会。我们通过这些研讨会获得的结果发表在这些研讨会的会议记录中。

项目成果

中村郁: "Stabilities of degenerate abelian varieties"Inventiones Math. 136. 659-715 (1999)

Iku Nakamura：“退化阿贝尔簇的稳定性”发明数学 136. 659-715 (1999)

森田康夫: "整数論"東京大学出版会. 277 (1999)

森田康夫：《数论》东京大学出版社277（1999）。

橋本光靖: "Good filtrations of symmetric algebras and strong F-regularity of invariant subrings"Mathematische Zeitschrift. (出版予定).

Mitsayasu Hashimoto：“对称代数的良好过滤和不变子环的强 F 正则性”Mathematische Zeitschrift（即将出版）。

隅広秀康: "Determinantal varieties associated to rank two vector bundles on projective spaces and splitting theorems" Hiroshima Math.J. 出版予定. (1999)

Hideyasu Sumihiro：“与射影空间上的两个向量束相关的行列式簇”和分裂定理”Hiroshima Math.J. 待出版。

佐藤栄一: "Smooth projective vavieties swept out by large dimersional linear spaces" 東北数学雑誌. 49. 299-321 (1997)

Eiichi Sato：“大维线性空间扫过的平滑射影星系”东北数学杂志 49. 299-321 (1997)。