平面二次线束的研究

STUDY ON PENCIL OF PLANE QUADRATIC LINES

平面二次线束是研究平面三次代数曲线和高次曲线的基础。欲系统地研究高次曲线,必须从研究二次线束着手。本文系统地研究平面二次线束的构成及分类,分析平面二次线束的退化情况和几何意义,给出了两类平面二次线束的判别方法。

The pencil of plane quadratic lines is the foundation for studying plane cubic curve and hig-her plane curves.To study sysetematieally higher plane curves must begin with pencil of planequadratic lines.In the paper the construction of pencil of plane quadratic lines and the geometricsignificance of its confficient are presented.The degenerate pencil of plane quadratic lines is ana-lysed so that the classification problem of pencil of plane quadratic lines is solved.