UNDERSTANDING SCHUBERT'S BOOK(Ⅲ)  

作　　者：Banghe LI 李邦河(KLMM,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]KLMM,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Acta Mathematica Scientia》2022年第2期437-453,共17页数学物理学报（B辑英文版）

基　　金：supported by National Center for Mathematics and Interdisciplinary Sciences,CAS。

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 

分 类 号：O18[理学—数学]