Teichmueller groupoids and monodromy in conformal field theory

共形场论中的 Teichmueller 群群和单峰

• 批准号: 13640031
• 负责人: ICHIKAWA Takashi
• 金额: $ 2.5万
• 依托单位: Saga University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640031/
• 关键词: Conformal field theory; Teichmueller groupoids; Monodromy representation; Bogomolov conjecture; Abelian varieties; Neron-Tate height functions; hypergeometric equations; Riemann surfaces; 超幾何学方程式; 代数曲線; モジュライ空間; ガロア表現; アラケロフ幾何

1. We described the monodromy representation of Teichmueller goupoids associated with conformal field theory. Extending Ullmo-Zhang's result on the Bogomolov conjecture, we gave a condition that a subvariety of an abelian variety is isomorphic to an abelian variety in terms of the value distribution of a Neron-Tate height function on the subvariety. We described the Riemann surfaces associated with the monodromy representation of hypergeometric equation with purely imaginary exponents.2. We gave an explicit formula of the Hasse unit index for the unit group of quadratic fields, and considered a Problem of Hasse for the ring of integers in certain abelian fields.3. We tried to justify the perturbative Chern-Simons theory using the asymptotic expansion theory via infinite dimensional stochastic analysis, and derived a simple Homfly polynomial.4. We showed that for certain algebraic geometry codes, the minimum distance are equal to the Fang-Rao bound, and found an algebraic geometry code of other type with same property.5. We gave the upper bound for the average number of connected components of the induced subgraphs of the graphs for simplicial polytopes, and proved that the arithmetical rank is equal to the projective dimension for the almost complete intersection Stanley-Reisner ideals.6. We calculated the virtual cohomological dimension and the Euler number of the mapping class group of a three-dimensional handlebody.

1。我们描述了与保形场理论相关的Teichmueller goupoids的单肌表示。扩大了ullmo-zhang在Bogomolov猜想上的结果，我们给出了一个条件，即在亚伦州的高度分布上，亚伯利亚品种的亚变量与亚伯利亚品种同构是同构的。我们描述了与纯粹假想指数的超几何方程的单层表示相关的riemann表面。2。我们为二次场单元组的HASSE单元索引提供了明确的公式，并考虑了某些Abelian字段中整数的Hasse问题。3。我们试图通过无限维度随机分析使用渐近扩展理论来证明扰动的Chern-Simons理论是合理的，并得出了一个简单的Homfly多项式。4。我们表明，对于某些代数几何代码，最小距离等于fang-rao结合，并找到了具有相同属性的其他类型的代数几何代码5。我们给出了图形诱导子图的连接组件的平均数量的上限，用于简单多面体，并证明算术等级等于几乎完整的交叉点Stanley-Reisner理想的投影尺寸。6。我们计算了三维手柄机构的映射类组的虚拟同谋维度和欧拉数。

项目成果

Hyeong-Kee Song and Tsuyoshi Uehara: "On the Feng-Rao bound for the minimum distance of certain algebraic geometry codes"Kyushu J. Math.. Vol.56. 405-418 (2002)

Hyun-Kee Song 和 Tsuyoshi Uehara：“关于某些代数几何代码的最小距离的 Feng-Rao 界”九州 J. Math.. Vol.56。

Y.Matoda, Toru Nakahara, S.I.A.Shah: "On a problem of Hasse for certain imaginary abelian fields"J. Number Theory. 96. 326-334 (2002)

Y.Matoda、Toru Nakahara、S.I.A.Shah：“关于某些想象的阿贝尔域的 Hasse 问题”J.

S.I.A.Shah, Toru Nakahara: "Monogenesis of the rings of integers in certain imaginary abelian fields"Nagoya Math. J.. 168. 85-92 (2002)

S.I.A.Shah，Toru Nakahara：“某些想象的阿贝尔域中整数环的单生性”名古屋数学。

Y. Motoda, T. Nakahara, S. I. A. Shah: "On a Problem of Hasse for certain imaginary abelian fields"J. Number Theory. Vol.96. 326-334 (2002)

Y. Motoda、T. Nakahara、S. I. A. Shah：“关于某些想象的阿贝尔域的 Hasse 问题”J.

Takashi Ichikawa: "Teichmueller groupoids and Galois action"J. Reine Angew. Math.. (to appear).

Takashi Ichikawa：“Teichmueller 群群和伽罗瓦作用”J.