Fundamental group of Galois covers of degree 5 surfaces

Meirav Amram, Cheng Gong, Mina Teicher, Wan-Yuan Xu

Published 2016-10-30Version 1

Let $X$ be a surface of degree $5$, which is considered as a branch cover of $\mathbb{CP}^2$ with respect to a generic projection. The surface has a natural Galois cover with Galois group $S_n$. In this paper, we compute the fundamental groups of Galois covers of degree $5$ that degenerate to nice plane arrangements; each of them is a union of five planes such that no three planes meet in a line. As an application, we give a counter-example of a question of Liedtke \cite[Question\,3.4]{Li08}.