Uniformization Theorems on Manifolds

流形上的均匀化定理

• 批准号: 08454015
• 负责人: FUTAKI Akito
• 金额: $ 2.69万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08454015/
• 关键词: Einstein metrics; Futaki Character; Minimal hypersurface; Singularity; Algebraic variety; 対称空間

Futaki studied on the relationship between the existence of Kaehler-Einstein metrics, stability of algebraic manifolds in the sense of Mumford and the nontriviality of the Futaki character.Tanno studied on the conjecture that there would not exist any L^2 harmonic forms on complete stable minimal hypersurfaces in Euclideam (m+1)-space, and proved affirmatively for m<5.Ishii constructed canonical models, minimal models and logarythmic canonical models for arbitrary nondegenerate hypersurface singularities. She also constructed minimal models for divisors of toric varieties. She construted a counter-example to a conjecture of Reid concerning canonical singularities. Tsuji analyzed the structure of canonical rings using singular metrics. He considered a construction of the moduli spaces of algebraic varieties of general type.Hattori considered the case where the holonomy groups induced by the projevtive structures on Riemann sufaces are discrete, and showed that only pseudo Fuchsian groups can appear when they are stable.

Futaki研究了Kaehler-Einstein的存在之间的关系，在Mumford的意义上，代数流形的稳定性与Futaki特征的非平底行为。构建了用于任意非排定超表面奇点的构建规范模型，最小模型和逻辑典型模型。她还为感谢您的品种的分裂构建了最小模型。她将反示例局限于REID的猜想，内容涉及规范奇异性。 Tsuji使用奇异指标分析了规范环的结构。他考虑了一般类型代数品种的模量空间的结构。哈托里考虑了这种情况，即在riemann sufaces上诱导的自动组群体是离散的，并且表明只有伪紫chs群在稳定时才能出现。

项目成果

S.Tanno: "L^2 harmonic forms and stability of minimal hypersurfaces" Journal of Mathematical Society of Japan. 48. 761-768 (1996)

S.Tanno：“L^2 调和形式和最小超曲面的稳定性”日本数学会杂志。

加藤和也,黒川信重,斉藤毅: "数論1" 岩波書店, 180 (1996)

加藤和也、黑川伸茂、斋藤武：《数论1》岩波书店，180（1996）

H.Tsuji: "Global generation of adjoint bundles" Nagoya Math.J.142. 5-16 (1996)

H.Tsuji：“伴随丛的全局生成”Nagoya Math.J.142。

T.Hattori: "Non-combability of Hilbert modulas groups" Communications in Analysis and Geometry. 3. 223-251 (1995)

T.Hattori：“希尔伯特模群的不可组合性”分析和几何中的通信。

T.Hattori: "Non-combability of Hilbert modular groups" Communications in Analysis and Geometry. 3. 223-251 (1995)

T.Hattori：“希尔伯特模群的不可组合性”分析和几何中的通信。