Understanding Schubert's Book (II)

doi:10.1007/s10473-022-0101-4

	Understanding Schubert's Book (II)
	Li, Banghe
刊名	ACTA MATHEMATICA SCIENTIA
	2021-08-25
页码	48
关键词	Hilbert Problem 15 enumeration geometry blow-up
ISSN号	0252-9602
DOI	10.1007/s10473-022-0101-4
英文摘要	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.
资助项目	National Center for Mathematics and Interdisciplinary Sciences, CAS
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000688482900023
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59214]
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.