Canonical maps of surfaces defined by Abelian covers

Abstract

In this paper, we classified the surfaces whose canonical maps are abelian covers over $\mathbb{P}^2$. Moveover, we construct a new Campedelli surface with fundamental group $\mathbb{Z}_2^{\oplus 3}$ and give defining equations for Perssson's surface and Tan's surfaces with odd canonical degrees explicitly.

Comments welcome