Castelnuovo Curves and Unobstructed Deformations.
Chow categories
Chow groups with coefficients.
Chow Motif and Higher Chow Theory of G/P.
Chow ring of projective nonsingular torus embedding
Codimension Arithmetically Gorenstein Subschemes of projective -space
We study the lowest dimensional open case of the question whether every arithmetically Cohen–Macaulay subscheme of is glicci, that is, whether every zero-scheme in is glicci. We show that a general set of points in admits no strictly descending Gorenstein liaison or biliaison. In order to prove this theorem, we establish a number of important results about arithmetically Gorenstein zero-schemes in .
Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)
2000 Mathematics Subject Classification: Primary 14E15; Secondary 14C05,14L30.In this note we attempt to generalize a few statements drawn from the 3-dimensional McKay correspondence to the case of a cyclic group not in SL(3, C). We construct a smooth, discrepant resolution of the cyclic, terminal quotient singularity of type 1/r(1,1,r−1), which turns out to be isomorphic to Nakamura’s G-Hilbert scheme. Moreover we explicitly describe tautological bundles and use them to construct a dual basis to...
Compactifications des espaces de configuration dans les schémas de Hilbert
Soient le complémentaire de l’union des diagonales dans et un quotient (éventuellement trivial) de par un sous-groupe du groupe symétrique . Ce travail présente des procédés de compactification de dans des produits de schémas de Hilbert. Notre démarche généralise et unifie des constructions classiques dues à Schubert-Semple, LeBarz-Keel, Kleiman et Cheah. Une étude géométrique plus détaillée est faite pour les cas . Cette étude inclut notamment une classification complète, la détermination...
Components of the Hilbert Scheme of Smooth space curves with the expected number of moduli.
Comptage de courbes sur le plan projectif éclaté en trois points alignés
Nous établissons une version de la conjecture de Manin pour le plan projectif éclaté en trois points alignés, le corps de base étant un corps global de caractéristique positive.
Concerning the existence of nice components in the Hilbert scheme of curves in ...n for n = 4 and 5.
Construction of space curves with good properties.
Contraction of excess fibres between the McKay correspondences in dimensions two and three
The quotient singularities of dimensions two and three obtained from polyhedral groups and the corresponding binary polyhedral groups admit natural resolutions of singularities as Hilbert schemes of regular orbits whose exceptional fibres over the origin reveal similar properties. We construct a morphism between these two resolutions, contracting exactly the excess part of the exceptional fibre. This construction is motivated by the study of some pencils of K3 surfaces appearing as minimal resolutions...
Contribution des droites d'une surface à ses multisécantes
Courbes gauches et modules de Rao.
Courbes rationnelles sur les variétés homogènes
Soit une variété homogène sous un groupe . Nous étudions les orbites maximales de sous l’action d’un parabolique de . Nous les décomposons en fibrations affines et projectives. Cette description permet de montrer que le schéma de Hilbert des courbes rationnelles lisses de classe fixée est non vide et irréductible.
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...