The global geometry of moduli spaoes

模数 spaoes 的全局几何

• 批准号: 16204001
• 负责人: NAKAMURA Iku
• 金额: $ 27.96万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16204001/
• 关键词: McKay correspondence; Moduli; Compactification; Rigid geometry; p-adic geometry; Mumford fake projective plane; K3 Surfaces; L-function; アーベル多様体; flux予想; 安定性; モジュライのコンパクト化; 複素超球の算術商; テータ関数; モジュライ空間; 群軌道のヒルベルト・スキーム; 3次曲面,複素超球; 2次超曲面

Nakamura proved a new theorem on McKay correspondence of a simple singularity C2/G, G being a finite group of SL(2,C). The theorem shows certain natural modules V and Vdagger have simple structures. Among others, the structure of Vdagger explains completely the known bijetive correspondence of the extended Dynkin diagram and all the irreducible representations of G.. The paper is now in print. He also proved an important vanishing theorem for degenerate quasi-abelian varieties.Weng is constructing a new important theory of geometric class field theory, which is modeled after Mumford's stability of GIT, Seshadri-Narashiman's theory of unitary vector bundles. In this program he defined nonabelian L-functions, and in some cases he proved a theorem analogous to Riemann hypothesis.Kato studied with Fujiwara the fundamental theory of p-adic geometry and rigid geometry. He proved also that Mumford fake projective plane and the other known fake projective planes are among Shimura varieties.Kondo constructed a uniformization by a 5-dimensional complex ball of the moduli of ordered 8 points of the projective line, by using Borcherds modular forms.Matsumoto gave a very precise description of a link and its complement in S3 by using real theta functions.Yoshioka proved a formula of counting the number of instantons on certain complex surfaces with Nakajima.

Nakamura证明了一种关于McKay对应的新定理，简单的奇异性C2/G，G是SL（2，C）的有限群。定理显示某些天然模块V和Vdagger具有简单的结构。除其他外，Vdagger的结构完全解释了扩展的Dynkin图的已知生物汇合对应关系以及G. G. G.的所有不可减至的表示。他还证明了一个重要的消失定理，用于堕落的准阿贝尔品种。温构建了一种新的几何阶层阶层理论的重要重要理论，该理论以芒福德（Mumford）的git稳定性，seshadri-narashiman的单位矢量套件理论进行了建模。在该计划中，他定义了非亚伯L功能，在某些情况下，他证明了与Riemann假设类似的定理。卡托用富士夫研究了P-Adic几何学和刚性几何学的基本理论。他还证明了芒村品种中的蒙福德假射飞机和其他已知的伪造的投射平面。昆多通过使用Borcherds模块化的形式构建了5维复合体的统一化，该模量的8点订购了投射线的8点。Matsumoto提供了一种非常精确的链接，并提供了链接的描述。计算与中岛某些复杂表面上的Instantons数量的数量。

项目成果

On the moduli of quiver representations associated with brane tilings

关于与膜平铺相关的颤动表示的模数

• 发表时间: 2007
• 作者: 北臺如法;隅広秀康;Akira Ishii;Akira Ishii;石井 亮;石井 亮;Akira Ishii;Akira Ishii;北臺如法;石井 亮;石井 亮
• 通讯作者: 石井 亮

Arithmetic Hilbert-Samuel formula

算术希尔伯特-塞缪尔公式

• 发表时间: 2007
• 作者: Shintaro;Kobayasi;Kazuhiro;Sakurai;Tsuyoshi;Mizunoya;Yoshiro;Higano;F.Suekane;森脇 淳
• 通讯作者: 森脇 淳

Moduli of K3 surfaces and complex ball quotients

K3 曲面的模和复数球商

• 发表时间: 2007
• 期刊: Progr. in Math. (Birkhauser) Vol.260
• 作者: Arai;T.;Nakata;Y.;Hodoshima;N.;and Kurisu;K.;Shigeyuki Kondo
• 通讯作者: Shigeyuki Kondo

Moduli of vector bundles on algebraic surfaces

代数曲面上向量丛的模

• 发表时间: 2007
• 期刊: Sugaku Expositions Vol.20
• 作者: Arai;T;Nakata;Y;Hodoshima;N;Kurisu;K;Kota Yoshioka
• 通讯作者: Kota Yoshioka

Isotropy representation for Harish-Chandra modules

Harish-Chandra 模块的各向同性表示

• 发表时间: 2005
• 期刊: Infinite Dimensional Harmonic Analysis III
• 作者: Matsuura;N;Iitaka;K;山下 博
• 通讯作者: 山下 博