Realization of symplectic cyclic actions on elliptic surfaces

Abstract

In this paper, we studythe existence of pseudofree, homologically trivial, symplecticcyclic actions $\mathbf{Z}_p$ with order $7<p\leq40$ on ellipticsurfaces $E(n)$. Especially,  we construct the $\mathbf{Z}_{13}$action on $E(n)$ and give the local representations of fixed points.