Special Fibres and Critical Locus for a Pencil of Plane Curve Singularities |
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Authors: | F. Delgado H. Maugendre |
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Affiliation: | (1) Dpto. Algebra, Geometría y Topología, Universidad de Valladolid, 47005 Valladolid, Spain;(2) Institut Fourier, Université de Grenoble I, BP 74, F-38402 Saint-Martin dHères, France |
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Abstract: | We will analyze the relationships between the special fibres of a pencil of plane curve singularities and the Jacobian curve J of (defined by the zero locus of the Jacobian determinant for any fixed basis ). From the results, we find decompositions of J (and of any special fibre of the pencil) in terms of the minimal resolution of . Using these decompositions and the topological type of any generic pair of curves of , we obtain some topological information about J. More precise decompositions for J can be deduced from the minimal embedded resolution of any pair of fibres (not necessarily generic) or from the minimal embedded resolution of all the special fibres. |
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Keywords: | critical locus Jacobian curve pencils plane curve singularities special fibre. |
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