UNDERSTANDING SCHUBERT'S BOOK (II)

doi:10.1007/s10473-022-0101-4

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (1): 1-48.doi: 10.1007/s10473-022-0101-4

• 论文 • 下一篇

UNDERSTANDING SCHUBERT'S BOOK (II)

李邦河

KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

收稿日期:2020-11-26 修回日期:2021-03-01 出版日期:2022-02-25 发布日期:2022-02-24
作者简介:Banghe Li,E-mail:libh@amss.ac.cn
基金资助:
This work was partially supported by National Center for Mathematics and Interdisciplinary Sciences, CAS.

UNDERSTANDING SCHUBERT'S BOOK (II)

Banghe LI

KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

Received:2020-11-26 Revised:2021-03-01 Online:2022-02-25 Published:2022-02-24
Supported by:
This work was partially supported by National Center for Mathematics and Interdisciplinary Sciences, CAS.

摘要/Abstract

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

Abstract: 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.

Key words: Hilbert Problem 15, enumeration geometry, blow-up

中图分类号:

14H50

李邦河. UNDERSTANDING SCHUBERT'S BOOK (II)[J]. 数学物理学报(英文版), 2022, 42(1): 1-48.

Banghe LI. UNDERSTANDING SCHUBERT'S BOOK (II)[J]. Acta mathematica scientia,Series B, 2022, 42(1): 1-48.

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UNDERSTANDING SCHUBERT'S BOOK (II)

UNDERSTANDING SCHUBERT'S BOOK (II)

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