Complete intersection singularities of splice type as universal Abelian covers.
Complex surface singularities with integral homology sphere links.
Computing limit linear series with infinitesimal methods
Alexander and Hirschowitz determined the Hilbert function of a generic union of fat points in a projective space when the number of fat points is much bigger than the greatest multiplicity of the fat points. Their method is based on a lemma which determines the limit of a linear system depending on fat points approaching a divisor.Other Hilbert functions were computed previously by Nagata. In connection with his counter-example to Hilbert’s fourteenth problem, Nagata determined the Hilbert function...
Conditions d'adjonction, d'après Du Val
Construction géométrique de la correspondance de McKay
Courbure et singularités complexes.
Coxeter-Dynkin diagrams of fat points in C² and of their stabilizations.
Coxeter-Dynkin diagrams of the complete intersection singularities Z9 and Z10.
Curves in P2(C) with 1-dimensional symmetry.
In a previous paper we showed that the existence of a 1-parameter symmetry group of a hypersurface X in projective space was equivalent to failure of versality of a certain unfolding. Here we study in detail (reduced) plane curves of degree d ≥ 3, excluding the trivial case of cones. We enumerate all possible group actions -these have to be either semisimple or unipotent- for any degree d. A 2-parameter group can only occur if d = 3. Explicit lists of singularities of the corresponding curves are...
Cycle exceptionnel de l’éclatement d’un idéal définissant l’origine de et applications
Soit un idéal de définissant l’origine de . On donne une méthode explicite pour déterminer, après un choix convenable des générateurs de , le cycle de sous-jacent à la fibre exceptionnelle de l’éclatement de relativement à . On étudie également l’éclatement d’une famille équimultiple d’idéaux ponctuels paramétrée par un germe d’espace analytique complexe réduit.
Cycles évanescents d’une fonction de Liouville de type
On construit un transport transverse aux fibres d’une fonction multivaluée de type ( complexes), à l’origine de . Ce transport est unique à isotopie près. On en déduit l’existence de voisinages réguliers dans lesquels les fibres sont toutes difféomorphes (voire dans un cas quasi-homogène, analytiquement difféomorphes). On obtient également une généralisation de la notion de monodromie. On calcule enfin l’homologie évanescente de la fibre-type, en précisant le gradué qui lui est associé.
Cyclic coverings of Fano threefolds
We describe a series of Calabi-Yau manifolds which are cyclic coverings of a Fano 3-fold branched along a smooth divisor. For all the examples we compute the Euler characteristic and the Hodge numbers. All examples have small Picard number .
Defects of Cusp Singularities.
Defects of cusp singularities and the classification of Hilbert modular threefolds.
Deformation of Complete Intersections with Singularities.
Deformations of theta divisors and the rank 4 quadrics problem
Degenerations of moduli of stable bundles over algebraic curves
Derivations of Negative Weight and Non-Smoothability of Certain Singularities.
Determination of the poles of the topological zeta function for curves.
Die Hierarchie der 1-modularen Singularitäten.