Finitely presented kernels of right-angled Artin groups with abelian quotients

In this article, we characterise when the kernels of right-angled Artin groups with abelian quotients are finitely generated and finitely presented – exhibiting an explicit finite generating set and finite presentation. As an application, we deduce the finite presentation of the kernel of any character of a right-angled Artin group. These results generalise the presentation of the kernel of a rational character of a right-angled Artin group given by Casals–Kazachkov–Roy and Dicks and Leary’s presentations of Bestina–Brady groups.