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モジュラー多様体の数論的及び代数幾何的研究

模流形的算术和代数几何研究

基本信息

批准号：
04245107
负责人：
織田孝幸
金额：
$ 0.58万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research on Priority Areas
财政年份：
1992
资助国家：
日本
起止时间：
1992 至无数据
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-04245107/
关键词：
moduli space fundamental group braid group Teichmiiller group mopping class group

项目摘要

市川はショートキー一意化された局所体上の代数曲線の微分形式や周期積分の普遍表示を導き,応用として,ヤコビアンローカス上消えるジーゲルモジュラー形式の特徴付けや,KP方程式のP進体上の解の構成等を与えた。寺杣は東大・数理科学研究科の斎藤毅氏との共同の研究で,代数多様体の周期積分の行列式について一般的な結果を得た。中村は双曲型代数多様体の射影有限基本群のガロア群作用のもとでの剛性現象に注目し種々の結果を得た。織田と寺杣はArtinの組紐群のBurau表現のreductionの全射に関する一般的な結果を得た。これは三角形群(2次元双曲空間の中の)の指数有限の部分群の構成や,アッペルのF1型超幾何微分方程式の特異超平面上のみ分岐する射影空間上の有限部分岐複覆の構成等種々の応用をもつ。織田は松本真(数理解析研究所)との共同研究で,タイヒミュラー群の曲面群への作用の記述の研究を進め,タイヒミュラー群の相対ウエイトフィルトレイションについて下からのある評価を得た。ここで得られた結果より,その証明途中の種々の結果は次の段階で重要になる。織田と寺杣の共同研究および織田と松本の共同研究は,いずれもモノドロミー表現の像の決定に関する結果で,代数曲線のある種のモジュライ空間の既約性を示すことに使える。この他,織田は三重大教育学部の古関春隆氏とSU(2,1)のウィタッカー関数とL因子に関する共同研究をほぼ完成させた。代表者および分担者は,その他の協力者をまじえて,適宜京都に2,3日の日程で集まり研究を進めた。研究の進展する段階で相互の仕事の関連がより明確になった。

In Ishikawa city, the differential form of algebraic curve is generally expressed in terms of the number of cycles on the body of the local office, which is generally expressed in the form of algebraic curves, differential forms, cycles, differential forms, differential forms, differential forms In the Department of Mathematical and physical Sciences, the Department of Mathematical Science and Technology, the Department of Mathematical Science and Technology, the Department of Mathematical Science, and the general results of the determinant of algebraic polysomorphism. Nakamura hyperbolic algebraic polyhedron projective finite basic group, the action of the basic group, the effect of the hyperbolic algebraic polyhedron, the effect of the hyperbolic algebraic multi-body projective finite basic group, the effect of the hyperbolic algebraic polyhedron, the effect of the basic group, the effect of the hyperbolic algebraic multi-body projective group. The results of the Artin group Burau showed that the general results of the reduction group were good. The finite exponent of the quadratic hyperbolic space group (quadratic hyperbolic space) is divided into a finite part of the group, and the finite part of the F 1 hyperdifferential equation is covered by the finite part of the projective space on the special plane. Yoshida Matsumoto (Institute of numerical understanding and Analysis) has made a joint study, a record of the effect of the surface group on the surface group, and a record of the progress of the study. You can verify the results of the test results, and the results show that there are several kinds of results on the way, and the sub-stages of the results are critical. In the joint study of Takata, monasteries, monasteries, and Matsumoto, it is shown that the results of the experiments are determined, and the algebraic curves are used to show that the results of the experiments are not limited to the results of the experiments. He and Tian three major education departments have completed the joint research on the number of L-factors in the department of education, which is Su (2p1). The representative, the contributor, the coordinator, the co-ordinator, the advisable Kyoto, the calendar collection, the research team, and so on. In the course of the research, there is a clear understanding of the progress of the study.