Matrice magique associée à un germe de courbe plane et division par l'idéal Jacobien

Details Matrice magique associée à un germe de courbe plane et division par l'idéal Jacobien Matrice magique associée à un germe de courbe plane et division par l'idéal Jacobien

2007-08-07

arxiv.org/abs/0708.0990v1

Annales de l'Institut Fourier 3, 57 (2007) 919

Mathematics

Algebraic Geometry

Pr\'epublication math\'ematique n^o;716 du Laboratoire Jean-Alexandre Dieudonn\'e (Univ. de Nice-Sophia Antipolis)

Scientific paper

In the ring of holomorphic functions at the origin of C^2, we consider the
equation uf'_x+vf'_y=wf where f and w are given. We introduce intersection
multiplicities relative to w and f'_y along the branches of f, and we study the
solutions (u,v) using these valuations. As an application, we construct an
explicit functional equation satisfied by f.

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