Finite presentations for K\"ahler groups with arbitrary finiteness properties

TL;DR

This paper constructs explicit finite presentations for K"ahler groups with various finiteness properties, addressing a question posed by Suciu and expanding understanding of their algebraic structure.

Contribution

It provides the first explicit finite presentations for a broad class of K"ahler groups with arbitrary finiteness properties, a significant advancement in the field.

Findings

Explicit finite presentations for K"ahler groups with arbitrary finiteness properties.

Answers to Suciu's question on K"ahler groups.

Enhanced understanding of the algebraic structure of K"ahler groups.

Abstract

We construct the first explicit finite presentations for a family of K\"ahler groups with arbitrary finiteness properties, answering a question of Suciu.