On the Galois covers of degenerations of surfaces of minimal degree

TL;DR

This paper studies Galois covers of minimal degree surfaces in complex projective space, proving that for dimensions five and higher, these covers are simply-connected surfaces of general type.

Contribution

It establishes that Galois covers of minimal degree surfaces in high dimensions are simply-connected surfaces of general type, a new topological classification result.

Findings

Galois covers are simply-connected for n ≥ 5

Covers are surfaces of general type

Results apply to surfaces in n+1 dimensional space

Abstract

We investigate the topological structures of Galois covers of surfaces of minimal degree (i.e., degree n) in n+1 dimensional complex projective space. We prove that for n is greater than or equal to 5, the Galois covers of any surfaces of minimal degree are simply-connected surfaces of general type.