Sur le schéma de Hilbert des variétés de codimension dans à cône de Cohen-Macaulay
Sur le schéma de Hilbert d'une courbe plane
Sur les schémas définissant les courbes rationnelles lisses de ayant fibré normal et fibré tangent restreint fixés
Sur les variétés de dimension 3 de type général dont le diviseur canonique est numériquement positif.
Sur les zéro-cycles de certaines hypersurfaces munies d'un automorphisme
Sur l'image de l'application d'Abel-Jacobi de Bloch
Techniques de construction et théorèmes d'existence en géométrie algébrique IV : les schémas de Hilbert
The Betti numbers of the Hilbert scheme of ponts on a smooth projective surface.
The Chow rings of smooth complete -embeddings
The cohomology ring of the Hilbert scheme of 3 points on a smooth projective variety.
The coniveau filtration and non-divisibility for algebraic cycles.
The decomposition and specialization of algebraic families of vector bundles
The dimension of the Chow variety of curves
The Euler series of restricted Chow varieties
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...
The Hilbert scheme of space curves of small diameter
This paper studies space curves of degree and arithmetic genus , with homogeneous ideal and Rao module , whose main results deal with curves which satisfy (e.g. of diameter, ). For such curves we find necessary and sufficient conditions for unobstructedness, and we compute the dimension of the Hilbert scheme, , at under the sufficient conditions. In the diameter one case, the necessary and sufficient conditions coincide, and the unobstructedness of turns out to be equivalent to the...
The Hilbert schemes of degree three curves
The Hilbert-Chow morphism and the incidence divisor.
The moduli space of commutative algebras of finite rank
The moduli space of rank- commutative algebras equipped with an ordered basis is an affine scheme of finite type over , with geometrically connected fibers. It is smooth if and only if . It is reducible if (and the converse holds, at least if we remove the fibers above and ). The relative dimension of is . The subscheme parameterizing étale algebras is isomorphic to , which is of dimension only . For , there exist algebras that are not limits of étale algebras. The dimension calculations...