複素射影平面上の直線配置と絡み目のミルナー不変量の研究

复射影平面上线排列和链接的Milner不变量研究

• 批准号: 15F15732
• 负责人: 田中 心
• 金额: $ 1.47万
• 依托单位: Tokyo Gakugei University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2015
• 资助国家: 日本
• 起止时间: 2015-10-09 至 2018-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15F15732/
• 关键词: 平面配置; 複素射影平面; ザリスキー対; 絡み目不変量; ミルナー不変量

本研究では，絡み目の不変量のアイデアを複素射影平面CP2内の直線配置の研究に応用して，直線配置の位相型を区別する新たな不変量を発見する事を目的とする．本年度は，主に次に上げる研究成果が得られた．これらの成果は，絡み目の不変量を応用した不変量を用いる事で得られた．（１）実射影変面内の直線配置に関して，図形的に計算可能な絡み数の構成に成功した．これまでの，絡み数は，その計算をコンピューターに依存しなければならない複雑なものばかりであった．ここで構成した絡み数は，計算が簡易であるというばかりでなく，これまで３例しか知られていなかったザリスキー対に加えて，新たに１０例のザリスキー対の構成に成功した．さらに，この結果は，今まで知られていなかった有理ザリスキー対の初めての例でもある．（２）直線配置の絡み数の研究を進め，k-アルタル曲線（k ∈ {3, 4, 5, 6}）に対してザリスキー対の存在を示した．（直線配置の研究においては，ザリスキー対と呼ばれる直線配置対の発見は，大変重要である．）（３）上で用いた絡み数は，Shimada k-pletと呼ばれる直線配置を区別する事を示した．これらの２つの論文の結果を通して，絡み数が区別する直線配置の特徴が明らかになった．２つ目の結果を得る為に，これまでの絡み数を，代数的・幾何的に再構築し，代数的な計算方法を備えた分離数と関連付けた．（４）基本群は，直線配置の組合せ的構造では，定まらない事を示した．これは，Falk氏とRandell氏の挙げた問題の解答を与えた事になる．また，ここで用いた証明は，Suciu氏の挙げた問題に否定的解答を与えた．

The purpose of this study is to increase the amount of information in the study of linear configuration in the projective plane of CP2. In the area of phase configuration, there is a lot of information on the purpose of this study. this year, the main and secondary research results have been improved. In order to measure the number of users, you can obtain information in terms of information. (1) in the projective plane, there is a straight line configuration in the plane, and the calculation of the shape of the image may be calculated as a result of success. The number of data, the number of data. It was calculated that there was a significant increase in the number of cases in which there was a significant increase in the number of cases, and 10 cases in the new case. the results show that there are significant differences between the two groups. (2) the study on the number of straight-line configuration is in progress. There is an indication of the existence of a straight line (k ∈ {3, 4, 5, 6}). The number of people using the number of users on the straight-line configuration (k ∈ {3,4,5,6}). Shimada k-plet calls for straight-line configuration to show how many things are available. In this section, you can read the results of this document. In the data section, you can see that the results of direct-line configuration are very clear. The results of this article show that the results of the results are not correct, that is, the number of cycles, the number of algebraic data, and the calculation method of algebra. (4) basic groups. In a straight-line configuration, you can make sure that you can find a solution to your problem, and that you will find a solution to your problem with Falk's Randell's question, and that you will find a solution to your problem with Suciu's question.

项目成果

On the topology of arrangements of a cubic and its inflectional tangents

立方体及其拐点切线的排列拓扑

• DOI: 10.3792/pjaa.93.50
• 发表时间: 2017
• 期刊: Proceedings of the Japan Academy, Series A, Mathematical Sciences
• 作者: Bannai Shinzo;Guerville-Balle Benoit;Shirane Taketo;Tokunaga Hiro-o
• 通讯作者: Tokunaga Hiro-o

A linking invariant for reducible curves

可约曲线的链接不变量

• 发表时间: 2016
• 作者: E. Artal;J.I. Cogolludo-Agustin;B. Guerville-Balle;M. Marco-Buzunariz;Christoffer Karlsson;Anton Frisk Kockum;B. Guerville-Balle;Anton Frisk Kockum;Benoit Guerville-Balle;Guerville-Balle Benoit;Anton Frisk Kockum;Guerville-Balle Benoit;Anton Frisk Kockum;Benoit Guerville-Balle;Anton Frisk Kockum;Benoit Guerville-Balle;Anton Frisk Kockum;Benoit Guerville-Balle
• 通讯作者: Benoit Guerville-Balle

Configuration of points and topology of real arrangements

实际排列的点配置和拓扑

• 发表时间: 2017
• 作者: E. Artal;J.I. Cogolludo-Agustin;B. Guerville-Balle;M. Marco-Buzunariz;Christoffer Karlsson;Anton Frisk Kockum;B. Guerville-Balle;Anton Frisk Kockum;Benoit Guerville-Balle;Guerville-Balle Benoit;Anton Frisk Kockum;Guerville-Balle Benoit
• 通讯作者: Guerville-Balle Benoit

On the I-invariant

关于 I 不变量

• 发表时间: 2016
• 作者: Guerville-Balle;Benoit
• 通讯作者: Benoit

Fundamental Groups of Real Arrangements and Torsion in the Lower Central Series Quotients

实数排列和下中央级数商中的扭转的基本群

• DOI: 10.1080/10586458.2018.1428131
• 发表时间: 2018
• 期刊: Experimental Mathematics
• 影响因子: 0.5
• 作者: Bartolo Enrique Artal;Guerville-Balle Benoit;Viu-Sos Juan
• 通讯作者: Viu-Sos Juan