Understanding Schubert's Book (II)

doi:10.1007/s10473-022-0101-4

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	Understanding Schubert's Book (II)
	Li, Banghe
	2021-08-25
发表期刊	ACTA MATHEMATICA SCIENTIA
ISSN	0252-9602
页码	48
摘要	In this paper, we give rigorous justification of the ideas put forward in 20, Chapter 4 of Schubert's book; a section that deals with the enumeration of conics in space. In that section, Schubert introduced two degenerate conditions about conics, i.e., the double line and the two intersection lines. Using these two degenerate conditions, he obtained all relations regarding the following three conditions: conics whose planes pass through a given point, conics intersecting with a given line, and conics which are tangent to a given plane. We use the language of blow-ups to rigorously treat the two degenerate conditions and prove all formulas about degenerate conditions stemming from Schubert's idea.
关键词	Hilbert Problem 15 enumeration geometry blow-up
DOI	10.1007/s10473-022-0101-4
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:000688482900023
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/59215
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 (II)[J]. ACTA MATHEMATICA SCIENTIA,2021:48.
APA	Li, Banghe.(2021).Understanding Schubert's Book (II).ACTA MATHEMATICA SCIENTIA,48.
MLA	Li, Banghe."Understanding Schubert's Book (II)".ACTA MATHEMATICA SCIENTIA (2021):48.