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. 我们描述了与共形场论相关的Teichmueller群似体的单态表示。推广了Ullmo-Zhang关于Bogomolov猜想的结果，我们给出了一个条件，即一个阿贝尔变体的一个子变体与一个阿贝尔变体在子变体上的Neron-Tate高度函数的值分布是同构的。我们描述了与纯虚指数超几何方程的单调表示有关的黎曼曲面。给出了二次域单位群的Hasse单位指标的显式公式，并考虑了若干阿贝尔域中整数环的Hasse问题。通过无限维随机分析，我们尝试用渐近展开理论来证明摄动chen - simons理论，并推导出一个简单的Homfly多项式。我们证明了某些代数几何码的最小距离等于Fang-Rao界，并发现了另一类具有相同性质的代数几何码。给出了简单多边形图的诱导子图的连通分量的平均数目的上界，并证明了几乎完全交Stanley-Reisner理想的算术秩等于投影维数。计算了三维柄体映射类群的虚上同调维数和欧拉数。

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.