Hilbert Problem 15 and Ritt-Wu Method (II)

doi:10.1007/s11424-020-9166-0

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	Hilbert Problem 15 and Ritt-Wu Method (II)
	Li, Banghe 1; Wang, Dingkang 1,2
	2020-08-04
发表期刊	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN	1009-6124
页码	15
摘要	This paper proves three statements of Schubert about cuspal cubic curves in a plane by using the concept of generic point of Van der Waerden and Weil and Ritt-Wu methods. They are relations of some special lines: 1) For a given point, all the curves containing this point are considered. For any such curve, there are five lines. Two of them are the tangent lines of the curve passing through the given point. The other three are the lines connecting the given point with the cusp, the inflexion point and the intersection point of the tangent line at the cusp and the inflexion line. 2) For a given point, the curves whose tangent line at the cusp passes through this point are considered. For any such curve, there are four lines. Three of them are the tangent lines passing through this point and the other is the line connect the given point and the inflexion point. 3) For a given point, the curves whose cusp, inflexion point and the given point are collinear are considered. For any such curve, there are five lines. Three of them are tangent lines passing through the given point. The other two are the lines connecting the given point with the cusp and the intersection point of the tangent line at the cusp and the inflexion line.
关键词	Cubic curves with cusp Hilbert problem 15 Ritt-Wu method
DOI	10.1007/s11424-020-9166-0
收录类别	SCI
语种	英语
资助项目	CAS Project[QYZDJ-SSW-SYS022]
WOS研究方向	Mathematics
WOS类目	Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000555391900006
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51898
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Banghe
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Li, Banghe,Wang, Dingkang. Hilbert Problem 15 and Ritt-Wu Method (II)[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2020:15.
APA	Li, Banghe,&Wang, Dingkang.(2020).Hilbert Problem 15 and Ritt-Wu Method (II).JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,15.
MLA	Li, Banghe,et al."Hilbert Problem 15 and Ritt-Wu Method (II)".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY (2020):15.