On the Galois covers of degenerations of surfaces of minimal degree

Abstract

We investigate the topological structures of Galois covers of surfaces of minimal degree (i.e., degree n) in double-struckCPn+1$\mathbb {CP}^{n+1}$. We prove that for n≥5$n\ge 5$, the Galois covers of any surfaces of minimal degree are simply‐connected surfaces of general type.