K3曲面上交错群A_5的作用

Effects of alternating group A_5 on K3 surfaces

以交错群A5在曲面上的作用为研究对象,从一类特殊的K3曲面的A5作用出发,得到了该类K3曲面上A5作用的不动点,利用不动点集计算了群作用的一些不变量H2(X;C),H2+(X;C)和H2-(X;C)。在此基础上,把其中的一些结果推广到了一般情形下的同伦K3曲面上,计算出当A5满足某些特定条件时的Direc算子G-指标及K-理论度。

The effect of alternating group As on K3 surfaces is taken as the research object, starting from some A5 action on a.special K3 surface, the fixed points set of this action and some invariants H2 （X; C）, H2^＋ （X; C） and H2^- （X; C） of the group action are obtained, and also some topological properties are obtained. Furthermore, it can be generalized to homotopy K3 surfaces, the G-index of Direc operator and K-theory degree are calculated.