平面四次曲线上的偶集

EVEN SET ON A PLANE CURVE OF DEGREE FOUR

运用编码的方法研究了平面四次曲线上的偶集,确定了偶集中通常二重点的个数,证明了四次既约平面曲线上偶集中包含4个通常二重点,并且任何5个通常二重点中必包含一个具有4个通常二重点的偶集,进一步证明了4个通常二重点构成偶集当且仅当这4个通常二重点处于一般位置。

This paper discussed even set on a plane curve of degree four by the coding method , and determined the number of nodes in an even set . It proved that any even set of nodes on a reduced plane curve of degree 4 contains 4 nodes ,and 5 nodes on this curve must contains an even set of 4 nodes .It also proved that 4 nodes on reduced plane curve of degree 4 form an even set if and only if these 4 nodes lie in general position.