射影平面上点的合冲  

Syzygies of Points in the Projective Plane

作　　者：莫佳丽 余琪 Mo Jiali;Yu Qi(Department of Mathematics,Soochow University,Suzhou 215006,China)

机构地区：[1]苏州大学数学科学学院,苏州215006

出　　处：《数学理论与应用》2021年第4期92-99,共8页Mathematical Theory and Applications

基　　金：联合基金(No.1171101006)“代数曲线和曲面分类的拓扑方法”资助。

摘　　要：本文主要研究射影平面上点的合冲问题.首先,针对射影平面上含7个不同点的集合X,给出其所有合冲的表达及其对应的饱和齐次理想I_(X)的极小自由分解.然后,在此基础上,根据线性系基点的数目和位置,结合前人的研究成果,对射影平面上所有的三次线性系进行分类,最终得到11种不同的三次线性系.In this paper,we mainly study the problem concerning the syzygies of points in the projective plane.Firstly,for a set X of 7 distinct points in the projective plane,we give the representations of all the syzygies,and the minimal free resolution of the corresponding saturated homogeneous ideal I_(X).Then based on the results and according to the number and position of the base points of the linear system,along with the known research results,we classify all the planar cubic linear systems,finally obtain 11 different planar cubic linear systems.

关 键 词：极小自由分解 齐次理想 代数曲线 三次线性系 基点 

分 类 号：O153.3[理学—数学]