椭圆曲面上不动点为二维实曲面的3阶循环群作用

Cyclic group action of order 3 on elliptic surface with 2-dimentional real surface as fixed point

设Z3为椭圆曲面E(2k)(k=1,2)上的3阶循环群作用,群作用的不动点为二维实连通曲面Σ.利用Seiberg-Witten不变量的有关结论,研究该不动曲面Σ的亏格g与自交数[Σ]·[Σ]之间的关系,得出反映两者关系的不等式.

Z3 is assumed as a cyclic group action of order 3 on elliptic surface E（2k） （k = 1,2）, and the fixed point of the group action is a 2-dimensional real connected surface ∑. By using relevant conclusions about the Seiberg-Witten invariants, the relationship between the genus g and the self intersection number [ ∑] · [ ∑] of the fixed surface 2 is studied, and an inequality reflecting the relationship between the two is obtained.