124350 20241125101127.0 doi 10.1002/mana.202100610 sideral 130576 ART-2023-130576 eng Cogolludo Agustín, José Ignacio Universidad de Zaragoza (orcid)0000-0003-1820-6755 Vanishing of higher order Alexander-type invariants of plane curves 2023 Access copy available to the general public Unrestricted The 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. info:eu-repo/grantAgreement/ES/DGA/E22-20R info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033 info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 0.8 2023 MATHEMATICS 179 / 490 = 0.365 2023 Q2 T2 0.625 2023 Mathematics (miscellaneous) 2023 Q2 1.5 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Elduque, Eva 2006 440 Universidad de Zaragoza Dpto. Matemáticas Área Geometría y Topología 296, 3 (2023), 1026-1040 Math. Nachr. Mathematische Nachrichten 0025-584X 262373 http://zaguan.unizar.es/record/124350/files/texto_completo.pdf Versión publicada 2273917 http://zaguan.unizar.es/record/124350/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:124350 articulos driver 2024-11-22-11:58:02 ARTICLE