A linking invariant for algebraic curves - Archive ouverte HAL
Article Dans Une Revue L'Enseignement Mathématique Année : 2020

A linking invariant for algebraic curves

Jean-Baptiste Meilhan

Résumé

We construct a topological invariant of algebraic plane curves, which is in somesense an adaptation of the linking number of knot theory. This invariant is shown tobe a generalization of the I -invariant of line arrangements developed by the first authorwith Artal and Florens. We give two practical tools for computing this invariant, using amodification of the usual braid monodromy or using the connected numbers introduced by Shirane. As an application, we show that this invariant distinguishes several Zariski pairs, i.e., pairs of curves having same combinatorics, yet different topologies. The former is the well known Zariski pair found by Artal, composed of a smooth cubic with 3 tangent lines at its inflexion points. The latter is formed by a smooth quartic and 3 bitangents.
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Dates et versions

hal-01287024 , version 1 (11-03-2016)

Identifiants

Citer

Benoît Guerville-Ballé, Jean-Baptiste Meilhan. A linking invariant for algebraic curves. L'Enseignement Mathématique , 2020, 66 (1), pp.63-81. ⟨10.4171/LEM/66-1/2-4⟩. ⟨hal-01287024⟩
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