Understanding Schubert's Book (III)

doi:10.1007/s10473-022-0201-1

CSpace

	Understanding Schubert's Book (III)
	Li, Banghe
	2022-03-01
发表期刊	ACTA MATHEMATICA SCIENTIA
ISSN	0252-9602
卷号	42 期号:2 页码:437-453
摘要	In 13 of Schubert's famous book on enumerative geometry, he provided a few formulas called coincidence formulas, which deal with coincidence points where a pair of points coincide. These formulas play an important role in his method. As an application, Schubert utilized these formulas to give a second method for calculating the number of planar curves in a one dimensional system that are tangent to a given planar curve. In this paper, we give proofs for these formulas and justify his application to planar curves in the language of modern algebraic geometry. We also prove that curves that are tangent to a given planar curve is actually a condition in the space of planar curves and other relevant issues.
关键词	Hilbert problem 15 enumeration geometry coincidence formula
DOI	10.1007/s10473-022-0201-1
收录类别	SCI
语种	英语
资助项目	National Center for Mathematics and Interdisciplinary Sciences, CAS
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000750822600001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59978
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	Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Banghe. Understanding Schubert's Book (III)[J]. ACTA MATHEMATICA SCIENTIA,2022,42(2):437-453.
APA	Li, Banghe.(2022).Understanding Schubert's Book (III).ACTA MATHEMATICA SCIENTIA,42(2),437-453.
MLA	Li, Banghe."Understanding Schubert's Book (III)".ACTA MATHEMATICA SCIENTIA 42.2(2022):437-453.