Parameterizations of algebraic curves.
Plane curves as projections of non singular space curves.
Plane curves of genus p and degree 2p as projections of space curves of the same degree.
Plane curves with small linear orbits, I
The “linear orbit” of a plane curve of degree is its orbit in under the natural action of . In this paper we compute the degree of the closure of the linear orbits of most curves with positive dimensional stabilizers. Our tool is a nonsingular variety dominating the orbit closure, which we construct by a blow-up sequence mirroring the sequence yielding an embedded resolution of the curve. The results given here will serve as an ingredient in the computation of the analogous information for...
Plane projections of a smooth space curve
Let C be a smooth non-degenerate integral curve of degree d and genus g in over an algebraically closed field of characteristic zero. For each point P in let be the linear system on C induced by the hyperplanes through P. By one maps C onto a plane curve , such a map can be seen as a projection of C from P. If P is not the vertex of a cone of bisecant lines, then will have only finitely many singular points; or to put it slightly different: The secant scheme parametrizing divisors in...
Polar quotients and singularities at infinity of polynomials in two complex variables
Using the notion of the maximal polar quotient we characterize the critical values at infinity of polynomials in two complex variables. As an application we give a necessary and sufficient condition for a family of affine plane curves to be equisingular at infinity.
Preperiodic dynatomic curves for
The preperiodic dynatomic curve is the closure in ℂ² of the set of (c,z) such that z is a preperiodic point of the polynomial with preperiod n and period p (n,p ≥ 1). We prove that each has exactly d-1 irreducible components, which are all smooth and have pairwise transverse intersections at the singular points of . We also compute the genus of each component and the Galois group of the defining polynomial of .
Příspěvek k theorii tečen a asymptot křivek rovinných
Problème de Brill-Noether pour les fibrés de Steiner. Applications aux courbes gauches
Projective schemes with degenerate general hyperplane section.
Projective schemes with degenerate general hyperplane section. II.
Projectively Normal Line Bundles on K-Gonal Curves and Rational Surfaces
2000 Mathematics Subject Classification: 14H50.Here we prove the projective normality of several special line bundles on a general k-gonal curve.* The author was partially supported by MIURST and GNSAGA of INdAM (Italy) ** The author was partially supported by KOSEF # R01-2002-000-00051-0
Propriétés des diamètres des courbes géométriques
Propriétés des systèmes de coniques, dans lesquels se trouvent des conditions de perpendicularité entre diverses séries de droites
Propriétés des systèmes de coniques relatives, toutes, à certaines séries de normales en rapport avec d'autres lignes ou divers points