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Communication Dans Un Congrès Année : 2011

An Adapted Version of the Bentley-Ottmann Algorithm for Invariants of Plane Curves Singularities

Résumé

We report on an adapted version of the Bentley-Ottmann algorithm for computing all the intersection points among the edges of the projection of a three-dimensional graph. This graph is given as a set of vertices together with their space Euclidean coordinates, and a set of edges connecting them. More precisely, the three-dimensional graph represents the approximation of a closed and smooth implicitly defined space algebraic curve, that allows us a simplified treatment of the events encountered in the Bentley-Ottmann algorithm. As applications, we use the adapted algorithm to compute invariants for each singularity of a plane complex algebraic curve, i.e. the Alexander polynomial, the Milnor number, the delta-invariant, etc.
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Dates et versions

hal-00646566 , version 1 (30-11-2011)

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Madalina Hodorog, Bernard Mourrain, Joseph Schicho. An Adapted Version of the Bentley-Ottmann Algorithm for Invariants of Plane Curves Singularities. 11th International Conference on Computational Science and Its Applications (ICCSA), Jun 2011, Santander, Spain. pp.121-131, ⟨10.1007/978-3-642-21931-3_10⟩. ⟨hal-00646566⟩
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