Semicontinuity for representations of one-dimensional Cohen-Macaulay rings.
Semi-group conditions for affine algebraic plane curves with more than one place at infinity.
An interesting and open question is the classification of affine algebraic plane curves. Abhyankar and Moh (1977) completely described the possible links at infinity for those curves where the link has just one component, a knot. Such curves are said to have one place at infinity. The Abhyankar-Moh result has been of great assistance in classifying those polynomials which define a connected curve with one place at infinity. This paper provides a new proof of the Abhyankar-Moh result which is then...
Semigroup of Two Irreducible Algebroid Plane Curves.
Semigroups associated to singular points of plane curves.
Separating ideals in dimension 2.
Experience shows that in geometric situations the separating ideal associated with two orderings of a ring measures the degree of tangency of the corresponding ultrafilters of semialgebraic sets. A related notion of separating ideals is introduced for pairs of valuations of a ring. The comparison of both types of separating ideals helps to understand how a point on a surface is approached by different half-branches of curves.
Simple constructions of algebraic curves with nodes
Singularities of polar curves
Singularities with exact Poincaré complex but not quasihomogeneous.
We give examples of complete intersections in C3 with exact Poincaré complex but not quasihomogeneous using the classification of C.T.C. and the algorithm of Mora.
Smoothness and irreducibility of varieties of plane curves with nodes and cusps
Sobre la composición de los puntos triples de las curvas planas.
Sobre los puntos múltiples de las curvas planas algebráicas.
Some characteristic numbers for nodal and cuspidal plane curves of any degree.
Special effect varieties in higher dimension.
Here we introduce the concept of special effect varieties in higher dimension and we generalize to Pn, n ≥ 3, the two conjectures given in [2] for the planar case. Finally, we propose some examples on the product of projective spaces and we show how these results fit with the ones of Catalisano, Geramita and Gimigliano.
Spectral Pairs, Mixed Hodge Modules, and Series of Plane Curve Singularities.
Stable vector bundles over cuspidal cubics
We give a complete classification of stable vector bundles over a cuspidal cubic and calculate their cohomologies. The technique of matrix problems is used, similar to [2, 3].
Stratifizierung im Hilbertschema. I. Raumkurven mit Singularitäten.
Sur la réalité des points doubles des courbes gauches
Une courbe réelle peut avoir des points doubles ordinaires de trois types différents : des points doubles réels à tangentes réelles, des points doubles réels isolés dans le domaine réel et des points doubles imaginaires. Soient des entiers tels que (où désigne la borne de Castelnuovo). On construit une courbe réelle irréductible de degré , non dégénérée dans l’espace projectif (i.e. non contenue dans un hyperplan) ayant pour seules singularités points doubles réels à tangentes réelles,...
Sur les idéaux jacobiens des courbes planes
Le ème idéal jacobien itéré d’une courbe complexe algébroïde plane a même clôture intégrale que l’idéal jacobien d’un élément général du ième idéal jacobien itéré. Ce résultat ramène pour les idéaux ci-dessus les calculs de multiplicité à des calculs de longueur.
Sur les jacobiennes des courbes à singularités ordinaires.
Sur les modules des singularités des courbes planes