Perturbing plane cruve singularities.
We describe the singularity of all but finitely-many germs in a pencil generated by two germs of plane curve sharing no tangent.
Picard Groups of Singular Affine Curves over a Perfect Fields.
Pinceaux de courbes planes et invariants polaires
We study pencils of plane curves , t ∈ ℂ, using the notion of polar invariant of the plane curve f = 0 with respect to a smooth curve l = 0. More precisely we compute the jacobian Newton polygon of the generic fiber , t ∈ ℂ. The main result gives the description of pencils which have an irreducible fiber. Furthermore we prove some applications of the local properties of pencils to singularities at infinity of polynomials in two complex variables.
Plane curves whose singular points are cusps and triple coverings of p2.
Plücker conditions on plane rational curves.
Points rationnels de la courbe modulaire
On démontre que les seuls points rationnels sur de la courbe sont les pointes.En conséquence, il n’existe pas de courbe elliptique définie sur possédant un sous-groupe cyclique rationnel d’ordre .
Polynôme d'Hilbert-Samuel des clôtures intégrales des puissances d'un idéal m-primaire
Puiseux Expansion of a Cuspidal Singularity
We present an effective and elementary method of determining the topological type of a cuspidal plane curve singularity with given local parametrization.