Construction of space curves with good properties.
Courbe des trisecantes a une courbe lisse de P3 de degre d > 2g + 1.
Courbes entières dans les surfaces algébriques complexes
Courbes gauches et modules de Rao.
Courbes lisses sur les surfaces rationnelles génériques : un lemme d'Horace différentiel
Nous démontrons un lemme permettant d’étudier l’irréductibilité et la lissité (hors des singularités prescrites) de la courbe plane générique de degré passant par points génériques avec des multiplicités fixées par avance. Ce lemme repose sur la “méthode d’Horace”, introduite par A. Hirschowitz. Il est appliqué ici à l’étude des courbes de genre inférieur ou égal à .
Curves in P² and symplectic packings.
Curves on a double surface.
Let F be a smooth projective surface contained in a smooth threefold T, and let X be the scheme corresponding to the divisor 2F on T. A locally Cohen-Macaulay curve C included in X gives rise to two effective divisors on F, namely the largest divisor P contained in C intersection F and the curve R residual to C intersection F in C. We show that under suitable hypotheses a general deformation of R and P lifts to a deformation of C on X, and give applications to the study of Hilbert schemes of locally...
Curves on a ruled cubic surface.
For the general ruled cubic surface S (with a double line) in P3 = P3 sub k, k any algebraically closed field, we find necessary conditions for which curves on S can be the specialization of a flat family of curves on smooth cubics. In particular, no smooth curve of degree > 10 on S is such a specialization.
Curves on a smooth quadric.
We associate to every curve on a smooth quadric a polynomial equation that defines it as a divisor; this polynomial is defined through a matrix. In this way we can study several properties of these curves; in particular we can give a geometrical meaning to the rank of the matrix which defines the curve.
Curves on surfaces with multiple line.
Curves with finite turn
In this paper we study the notions of finite turn of a curve and finite turn of tangents of a curve. We generalize the theory (previously developed by Alexandrov, Pogorelov, and Reshetnyak) of angular turn in Euclidean spaces to curves with values in arbitrary Banach spaces. In particular, we manage to prove the equality of angular turn and angular turn of tangents in Hilbert spaces. One of the implications was only proved in the finite dimensional context previously, and equivalence of finiteness...
Cutting diagram method for systems of plane curves with base points
We develop a new method of proving non-speciality of a linear system with base fat points in general position. Using this method we show that the Hirschowitz-Harbourne conjecture holds for systems with base points of equal multiplicity bounded by 42.
De l'hélice osculatrice
Degenerate (r-2)-Dimensional subvarieties through the generic hyperplane section of a reduced irreducible complex curve in pr.
Détermination, par le principe de correspondance, de la classe de la développée et de la caustique par réflexion d'une courbe géométrique d'ordre m et de la classe n
Determining obstructions for space curves, with applications to non-reduced components of the Hilbert scheme.
Dimension of families of space curves
Doppeltangenten einer Curve nter Ordnung
Eight-secant conics for space curves.
Elementární spůsob vyšetřování křivek v rovině