doi:10.1002/mana.202100610engCogolludo Agustín, José IgnacioElduque, EvaVanishing of higher order Alexander-type invariants of plane curvesART-2023-130576The higher order degrees are Alexander-type invariants of complements to an affine plane curve. In this paper, we characterize the vanishing of such invariants for a curve given as a transversal union of plane curves ′ and ′′ in terms of the finiteness and the vanishing properties of the invariants of ′ and ′′, and whether or not they are irreducible. As a consequence, we prove that the multivariable Alexander polynomial Δmulti is a power of ( − 1), and we characterize when Δmulti = 1 in terms of the defining equations of ′ and ′′. Our results impose obstructions on the class of groups that can be realized as fundamental groups of complements of a transversal union of curves.2023http://zaguan.unizar.es/record/12435010.1002/mana.202100610http://zaguan.unizar.es/record/124350oai:zaguan.unizar.es:124350info:eu-repo/grantAgreement/ES/DGA/E22-20Rinfo:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033Mathematische Nachrichten 296, 3 (2023), 1026-1040by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess