Algebraic Geometry of Plane Curves

平面曲线的代数几何

• 批准号: 09440005
• 负责人: SAKAI Fumio
• 金额: $ 7.23万
• 依托单位: Saitama University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B).
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-09440005/
• 关键词: plane curve; rational curve; cuspidal curve; multiplicity sequence; quadratic transformation; place at infinity; projective equivalence; maximal multiplicity; 有理関数; 特異点解消; 重複度; 代数曲面; 変形; 有理尖点曲線; 巡回被覆; 特異点

The head investigator proved that for rational cuspidal plane curves of degree d, the degree d is less than or equal to the 3× the maximal multiplicity (Math.Ann. 285, (1989), 233-247). In the project, if the maximal multiplicity is equal to d-2, rational cuspidal plane curves are completely classified and the defining equations of the curves are determined (Osaka J.Math., 37, (2000), 405-415). As a corollary, it turns out that such rational cuspidal plane curves are transformable into a line by Cremona transformations. The systematic study of the effect of degenerate quadratic transformations on germs of plane curve singularities are used.The head investigator published a book on algebra (The theory of Rings and Fileds, Kyoritsu, 1997). Based on new concept, the theory of rings and fields are written to the study of algebraic geometry.

事实证明，对于D度D的有理尖曲线，D度小于或等于3×最大多重性（Math.ann。285，（1989），233-247）。在项目中，如果最大多样性等于D-2，则将有理尖曲线曲线完全分类，并确定曲线的定义方程（Osaka J.Math。，37，（2000），（2000），405-415）。作为推论，事实证明，这种有理的尖曲线曲线可以通过Cremona Transformations转化为一条线。使用了二次转化对平面曲线奇异性细菌的影响的系统研究。负责人研究者发表了一本关于代数的书（《指环与档案理论》，kyoritsu，1997年）。基于新概念，指环和田地理论写入代数几何学的研究。

项目成果

T.Fukui: "Blow-analytic equi-singularities,properties and progress" Real analytic and Algebraic singularies,Pitman Research. 381. 8-29 (1998)

T.Fukui：“吹解析等奇点、性质和进展”实解析和代数奇点，Pitman Research。

M. Djoric and M. Okumura: "CR submonifolds of maximal CR dimension of complex progective space"Math. Nachr.. 202. 17-28 (1999)

M. Djoric 和 M. Okumura：“复杂预想空间的最大 CR 维度的 CR 子流形”数学。

T.Fukui and J.Weyman: "Cohen Macaulay properties of Thoin Boarduion strata I"Proc.London Math.Soc.. 80. 257-303 (2000)

T.Fukui 和 J.Weyman：“Thoin Boarduion 地层 I 的科恩·麦考利性质”Proc.London Math.Soc.. 80. 257-303 (2000)

酒井文雄: "環と体の理論" 共立出版, 200 (1997)

酒井文雄：《环与体的理论》Kyoritsu Shuppan，200 (1997)

T.Fukui and L.Paunescu: "Modified analytic trivia lization for weighted homogeneous function-germs"J.of Math.Soc.Japan. 52. 433-446 (2000)

T.Fukui 和 L.Paunescu：“加权齐次函数细菌的改进分析平凡化”J.of Math.Soc.Japan。