On the holomorphic convexity of nilpotent coverings over compact K\"ahler surfaces

TL;DR

This paper investigates the conditions under which nilpotent coverings over compact K"ahler surfaces are holomorphically convex, establishing that such convexity holds if the covering has fewer than two ends, and analyzing the end structure of Malcev coverings.

Contribution

It proves holomorphic convexity of nilpotent regular coverings over compact K"ahler surfaces without two ends and shows Malcev coverings have at most one end, advancing understanding of their complex structure.

Findings

Nilpotent regular coverings over compact K"ahler surfaces are holomorphically convex if they have fewer than two ends.

Malcev coverings of compact K"ahler manifolds have at most one end.

Abstract

We prove that any nilpotent regular covering over a compact K\"ahler surface is holomorphically convex if it does not have two ends. Furthermore, we show that the Malcev covering of any compact K\"ahler manifold has at most one end.