Branched covers and Zariski pairs

分支盖和 Zariski 对

• 批准号: 19540043
• 负责人: TOKUNAGA Hiroo
• 金额: $ 2.83万
• 依托单位: Tokyo Metropolitan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540043/
• 关键词: Galois分岐被覆; ザリスキ・ペア; splitting curve; Mordell-Weil群; 相互法則; Zariski pair; non-Galois 3次被覆; 引き戻し構成; versal Galois被覆; 3次被覆; Alexander多項式; 基本群; 特異K3曲面

I have investigated branched Galois covers and Zariski pairs. With E.Artal Bartolo and J.-I.Cogolludo, I first wrote a survey article on Zariski pairs. In the survey, main tools and results about Zariski pair up until around 2007 are explained. Also some new results are contained in the survey. Afterward, I have studied 1. veral Galois covers and the two dimensional Cremona group, 2. non-Galois triple covers (a generalization of Zariski's example and pull-back constructions), and 3. splitting curves on double covers and their application to Zariski pairs.

我已经研究了分支伽罗瓦盖和Zorkiki对。与E.Artal Bartolo和J. I.Cogolludo，我第一次写了一篇关于Zagraki对的调查文章。在调查中，主要工具和结果关于Zki对直到2007年左右的解释。调查中也有一些新的结果。后来，我学习了1.几个伽罗瓦覆盖和二维克雷莫纳群，2。非伽罗瓦三重覆盖（Zorski的例子和拉回结构的推广），和3。双覆盖上的分裂曲线及其在Zapriki对上的应用

项目成果

A survey on Zariski pairs

• DOI: 10.2969/aspm/05010001
• 发表时间: 2006
• 作者: Enrique Artal Bartolo;J. Agustín;H. Tokunaga

A note on embeddings of S4 and A5 into the two-dimensional Cremona group and versal Galois covers

关于将 S4 和 A5 嵌入二维克雷莫纳群和通用伽罗瓦覆盖的注释

• 发表时间: 2007
• 期刊: Publ. Inst. Math. Sci. 43
• 作者: Shinzo Bannai;Hiro-o Tokunaga
• 通讯作者: Hiro-o Tokunaga

Splitting curves in double covers, Branched coverings

双覆盖、分支覆盖中的分割曲线

• 发表时间: 2009
• 作者: Shinzo Bannai;Hiro-o Tokunaga;Mutsuo Oka;Shinzo BANNAI and Hiro-o TOKUNAGA;Hirotaka Ishida Hiroo Tokunaga;徳永浩雄;徳永浩雄;徳永浩雄;島田伊知朗;徳永浩雄;徳永浩雄;徳永浩雄;徳永浩雄;徳永浩雄
• 通讯作者: 徳永浩雄

Triple covers of algebraic surfaces and a generalization of Zariski's example

代数曲面的三重覆盖和 Zariski 示例的推广

• 发表时间: 2009
• 期刊: Advanced Studies in Pure Math. 56
• 作者: Hirotaka Ishida;Hiro-o Tokunaga
• 通讯作者: Hiro-o Tokunaga

On Zariski pairs of normal surfaces in P3

关于 P3 中的 Zariski 法向曲面对

• 发表时间: 2009
• 作者: Shinzo Bannai;Hiro-o Tokunaga;Mutsuo Oka;Shinzo BANNAI and Hiro-o TOKUNAGA;Hirotaka Ishida Hiroo Tokunaga;徳永浩雄;徳永浩雄;徳永浩雄;島田伊知朗
• 通讯作者: 島田伊知朗