Research of Quasi-Kodaira singularities

准小平奇点的研究

• 批准号: 10640062
• 负责人: TOMARU Tadashi
• 金额: $ 0.58万
• 依托单位: Gunma University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640062/
• 关键词: singularity; degeneration; curve; pencil genus; geometric genus; 代数曲線の退化族; 基本サイクル; 有限巡回被覆; 基本種数

In this research, we have investigated the relation between degeneration of algeraic curves and normal surface singularities. First we gave the definiton of quasi-Kodaira singularities and gave some sufficient conditions for normal surface singularities to be quasi-Kodaira. Second we considered hypersuface normal surface singularities (namely, the equation is z^n=f(x,Y) ). For the class, we found an interesting class of quasi-Kodaira singularities. Third, we prove an interesting result about cyclic covers of normal surface singularities. Under some conditions, if the order of the group of the cyclic cover is sufficiently large, then the cyclic cover over a normal surface singularity is a quasi-Kodaira singularity. Fourth, we prove some formulae about geometric genus of elliptic quasi-Kodaira singularity.

在本研究中，我们研究了阿尔及利亚曲线的退化与法向曲面奇点之间的关系。首先给出了拟Kodaira奇点的定义，并给出了法向曲面奇点为拟Kodaira的充分条件。其次，我们考虑了超曲面的法曲面奇点（即方程z^n=f（x，Y））。对于类，我们发现了一个有趣的类的quasi-Kodaira奇点。第三，我们证明了一个有趣的结果，关于正规曲面奇点的循环覆盖。在一定条件下，若循环覆盖群的阶足够大，则法曲面奇点上的循环覆盖是拟Kodaira奇点。第四，我们证明了椭圆型拟Kodaira奇点的几何亏格的一些公式。

项目成果

都丸正: "On Kodaira singularities defined by Z^n=f(x,y)"Mathematische Zeitschrift (1999.10.アクセプト). (予定).

Tadashi Tomaru：“论由 Z^n=f(x,y) 定义的 Kodaira 奇点”Mathematische Zeitschrift（1999.10.已接受）（计划中）。

奥間智弘: "The second plon-qenus of surface sihgularlties" Compositio Math.110. 263-276 (1998)

Tomohiro Okuma：“表面结构的第二个 plon-qenus”Compositio Math.110 (1998)。

奥間智弘: "The pluri-genera of surface sihgularties" Tohoku Math. J.50. 115-132 (1998)

Tomohiro Okuma：“表面图形的多属”Tohoku Math J.50（1998）。

都丸正: "On Kodaira singularities defined by Z^n=f(x,y)"Mathematische Zeitshnft. (印刷中).

Tadashi Tomaru：“论由 Z^n=f(x,y) 定义的 Kodaira 奇点”Mathematische Zeitshnft（正在出版）。

T. Okuma: "The polynomial periodicity of pluri-genera of surface singularities"Saitama Math. J.. 17. 7-13 (1999)

T. Okuma：“表面奇点的多属多项式周期性”埼玉数学。