南京航空航天大学学报(英文版)
南京航空航天大學學報(英文版)
남경항공항천대학학보(영문판)
TRANSACTIONS OF NANJING UNIVERSITY OF AERONARUTICS AND ASTRONAUTICS
2002年
2期
203-207
,共5页
多项式向量场%线场%几何性质
多項式嚮量場%線場%幾何性質
다항식향량장%선장%궤하성질
polynomial vector fields%line fields%geome-tric properties
证明:在研究多项式系统的几何性质时,多项式系统应当定义成射影空间中奇点集之余维数至少为2的线场.在这个定义中,多项式系统的次数与通常的次数,在概念上不全相同,通常的n+1次退化系统属于这里的n次系统.值得注意的是,本文给出的定义与坐标系的选取无关,在这种定义下,多项式系统的某些几何性质变得非常明显.
證明:在研究多項式繫統的幾何性質時,多項式繫統應噹定義成射影空間中奇點集之餘維數至少為2的線場.在這箇定義中,多項式繫統的次數與通常的次數,在概唸上不全相同,通常的n+1次退化繫統屬于這裏的n次繫統.值得註意的是,本文給齣的定義與坐標繫的選取無關,在這種定義下,多項式繫統的某些幾何性質變得非常明顯.
증명:재연구다항식계통적궤하성질시,다항식계통응당정의성사영공간중기점집지여유수지소위2적선장.재저개정의중,다항식계통적차수여통상적차수,재개념상불전상동,통상적n+1차퇴화계통속우저리적n차계통.치득주의적시,본문급출적정의여좌표계적선취무관,재저충정의하,다항식계통적모사궤하성질변득비상명현.
This note shows that when studying geometric pro-perties, a polynomial system is defined as a line field on a projective space such that its singular set has co-dimension at least 2. By this definition, the concept of the degree of a polynomial system does not coincide with the usual one. The usual degenerate polynomial system of degree n+1 should be regarded as a system of degree n. Note that the definition is independent coordinate system. And, by this definition, some geometric properties concerning polynomial vector fields turn out to be evident.
