Sur les coniques qui passent par trois points et ont un double contact avec un cercle donné
Sur les courbes planes transcendantes, susceptibles de faire partie d’un système ()
Sur les invariants des pinceaux de formes quintiques binaires
On décrit l’algèbre des invariants de l’action naturelle du groupe sur les pinceaux de formes quintiques binaires.
Sur les polaires d'une droite relativement aux courbes et aux surfaces algébriques
Sur les schémas définissant les courbes rationnelles lisses de ayant fibré normal et fibré tangent restreint fixés
Sur quelques propriétés de l'hypocycloïde à 3 points de rebroussement
Sur trois coniques confocales deux à deux
Sur un théorème de Jacques Bernoulli
Sur un théorème de M. Chasles concernant les coniques homofocales
Syzygies and logarithmic vector fields along plane curves
We investigate the relations between the syzygies of the Jacobian ideal of the defining equation for a plane curve and the stability of the sheaf of logarithmic vector fields along , the freeness of the divisor and the Torelli properties of (in the sense of Dolgachev-Kapranov). We show in particular that curves with a small number of nodes and cusps are Torelli in this sense.
Ternary quartics and 3-dimensional commutative algebras.
The Abel-Jacobi map for cubic threefold and periods of Fano threefolds of degree 14.
The Apery algorithm for a plane singularity with two branches.
The dimension of the Chow variety of curves
The equations of space curves on a quadric.
The homogeneous ideals of curves in a double plane have been studied by Chiarli, Greco, Nagel. Completing this work we describe the equations of any curve that is contained in some quadric. As a consequence, we classify the Hartshorne-Rao modules of such curves.
The Genus of Curves in P4 and P5.
The Genus of Curves in P4 verifying certain Flag conditions.
The growth rate of the number of classes of real plane algebraic curves with the growth of the degree.
The Hilbert Function of curves on certain smooth quartic surfaces.
The Hilbert Scheme of Buchsbaum space curves
We consider the Hilbert scheme of space curves with homogeneous ideal and Rao module . By taking suitable generizations (deformations to a more general curve) of , we simplify the minimal free resolution of by e.g making consecutive free summands (ghost-terms) disappear in a free resolution of . Using this for Buchsbaum curves of diameter one ( for only one ), we establish a one-to-one correspondence between the set of irreducible components of that contain and a set of minimal...