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...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Universidad Autónoma de Madrid |
| Repository: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Language: | English |
| OAI Identifier: | oai:repositorio.uam.es:10486/705949 |
| Online Access: | http://hdl.handle.net/10486/705949 https://dx.doi.org/10.1002/mana.202100610 |
| Access Level: | Open access |
| Keyword: | Alexander invariants Alexander polynomials Derived series Line arrangements Plane curves Matemáticas |
| Summary: | 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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