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1 Department of Mathematics, Tokyo Gakugei University 2 IF - Institut Fourier

Abstract : We construct a topological invariant of algebraic plane curves, which is in some sense an adaptation of the linking number of knot theory. This invariant is shown to be a generalisation of the I-invariant of line arrangements developed by the first author with Artal and Florens. We give a practical tool for computing this invariant, using a modification of the usual braid monodromy. As an application, we show that this invariant distinguishes a new Zariski pair of curves, i.e. a pair of curves having same combinatorics, yet different topology. These curves are composed of a smooth cubic with 5 tangent lines at its inflexion points. As in the historical example of Zariski, this pair can be geometrically characterized by the mutual position of their singular points.

Author: Benoît Guerville-Ballé - Jean-Baptiste Meilhan -

Source: https://hal.archives-ouvertes.fr/


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