Vanishing of higher order Alexander-type invariants of plane curves
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...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/705949 |
| Acceso en línea: | http://hdl.handle.net/10486/705949 https://dx.doi.org/10.1002/mana.202100610 |
| Access Level: | acceso abierto |
| Palabra clave: | Alexander invariants Alexander polynomials Derived series Line arrangements Plane curves Matemáticas |
| Sumario: | 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 |
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