Camille Plénat (2008)
Annales de l’institut Fourier
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This paper deals with the Nash problem, which consists in comparing the number of families of arcs on a singular germ of surface with the number of essential components of the exceptional divisor in the minimal resolution of this singularity. We prove their equality in the case of the rational double points ().
Floric Tavares Ribeiro (2011)
Annales de l’institut Fourier
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A Brückner-Vostokov formula for the Hilbert symbol of a formal group was established by Abrashkin under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ()-modules and a cohomological interpretation of Abrashkin’s technique. To do this, we build ()-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas...
Wiesław Pawłucki (2008)
Annales de l’institut Fourier
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A continuous linear extension operator, different from Whitney’s, for -Whitney fields (p finite) on a closed o-minimal subset of is constructed. The construction is based on special geometrical properties of o-minimal sets earlier studied by K. Kurdyka with the author.
Ştefănescu, Mirela, Dumitru, Mariana (2002)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Laurent Evain (2007)
Annales de l’institut Fourier
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Alexander and Hirschowitz determined the Hilbert function of a generic union of fat points in a projective space when the number of fat points is much bigger than the greatest multiplicity of the fat points. Their method is based on a lemma which determines the limit of a linear system depending on fat points approaching a divisor. Other Hilbert functions were computed previously by Nagata. In connection with his counter-example to Hilbert’s fourteenth problem, Nagata determined...