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On the values of logarithmic residues along curves
We consider the germ of a reduced curve, possibly reducible. F.Delgado de la
Mata proved that such a curve is Gorenstein if and only if its semigroup of
values is symmetrical. We extend here this symmetry property to any fractional
ideal of a Gorenstein curve. We then focus on the set of values of the module
of logarithmic residues along plane curves or complete intersection curves,
which determines and is determined by the values of the Jacobian ideal thanks
to our symmetry theorem. Moreover, we give the relation with Kahler
differentials, which are used in the analytic classification of plane branches.
We also study the behaviour of logarithmic residues in an equisingular
deformation of a plane curve.Comment: To appear at Annales de l'Institut Fourier. Examples added. 27 page
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