数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (1): 97-113.doi: 10.1007/s10473-021-0106-4

• 论文 • 上一篇    下一篇

UNDERSTANDING SCHUBERT'S BOOK (I)

李邦河   

  1. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • 收稿日期:2019-11-12 修回日期:2020-03-29 出版日期:2021-02-25 发布日期:2021-04-06
  • 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 (I)

Banghe LI   

  1. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2019-11-12 Revised:2020-03-29 Online:2021-02-25 Published:2021-04-06
  • About author:Banghe LI,E-mail:libh@amss.ac.cn
  • Supported by:
    This work was partially supported by National Center for Mathematics and Interdisciplinary Sciences, CAS.

摘要: Hilbert Problem 15 required an understanding of Schubert’s book [1], both its methods and its results. In this paper, following his idea, we prove that the formulas in §6, §7, §10, about the incidence of points, lines and planes, are all correct. As an application, we prove formulas 8 and 9 in §12, which are frequently used in his book.

关键词: Hilbert Problem 15, enumeration geometry, incidence formula

Abstract: Hilbert Problem 15 required an understanding of Schubert’s book [1], both its methods and its results. In this paper, following his idea, we prove that the formulas in §6, §7, §10, about the incidence of points, lines and planes, are all correct. As an application, we prove formulas 8 and 9 in §12, which are frequently used in his book.

Key words: Hilbert Problem 15, enumeration geometry, incidence formula

中图分类号: 

  • 14H50