Cyclic group actions on elliptic surfaces E(2n)

Abstract

In this paper, we study the action of cyclic group $\mathbf{Z}_3$ on elliptic surfaces $E(2n), (n\geq1)$. For convenience, we  suppose the fixed point set of $\mathbf{Z}_3$ is composed of 2-spheres. We give a classification of this action. At the same time, we obtain the representation induced by $\mathbf{Z}_3$  on the second cohomology of $E(2n)$