Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes.
Eine Vervollständigung der Chowvarietät der Punktetripel
Einfacher Zusammenhang der Hilbertschemata von Kurven im komplex-projektiven Raum.
Einige einfach-zusammenhängende Hilbertschemata.
Elementary introduction to representable functors and Hilbert schemes
The purpose of this paper is to define and prove the existence of the Hilbert scheme. This was originally done by Grothendieck in [4]. A simplified proof was given by Mumford [11], and we will basically follow that proof, with small modifications.
Équivalence linéaire des idéaux de polynômes
Equivariant degenerations of spherical modules for groups of type
V. Alexeev and M. Brion introduced, for a given a complex reductive group, a moduli scheme of affine spherical varieties with prescribed weight monoid. We provide new examples of this moduli scheme by proving that it is an affine space when the given group is of type and the prescribed weight monoid is that of a spherical module.
Excess intersection of divisors
Families of reduced zero-dimensional schemes.
A great deal of recent activity has centered on the question of whether, for a given Hilbert function, there can fail to be a unique minimum set of graded Betti numbers, and this is closely related to the question of whether the associated Hilbert scheme is irreducible or not. We give a broad class of Hilbert functions for which we show that there is no minimum, and hence that the associated Hilbert sheme is reducible. Furthermore, we show that the Weak Lefschetz Property holds for the general element...
Familles maximales de systèmes de ponts surabondants dans P2.
Fano manifolds of degree ten and EPW sextics
O’Grady showed that certain special sextics in called EPW sextics admit smooth double covers with a holomorphic symplectic structure. We propose another perspective on these symplectic manifolds, by showing that they can be constructed from the Hilbert schemes of conics on Fano fourfolds of degree ten. As applications, we construct families of Lagrangian surfaces in these symplectic fourfolds, and related integrable systems whose fibers are intermediate Jacobians.
General Components of the Noether-Lefschetz Locus and their Density in the Space of all Surfaces.
General stable bundles arising as normal bundles of projective curves.
Generalization of Abel's theorem and some finiteness property of zero-cycles on surfaces
Generalized Castelnuovo Varieties.
Générateurs explicites du groupe de Chow du schéma de Hilbert des cubiques de IP(3, C).
Géométrie des schémas de Hilbert ponctuels
Groupe de Chow de codimension deux des variétés definies sur un corps de nombres: un théorème de finitude pour la torsion.
Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties.
Hilbert scheme of smooth space curves