Polynomial periodicity for Betti numbers of covering surfaces.
Polynomial-time computation of the degree of a dominant morphism in zero characteristic. II.
Principal polarizations of Prym-Tjurin varieties
Problèmes de modules pour les formes différentielles singulières dans le plan complexe.
Problemi di razionalità ed unirazionalità in geometria algebrica
Il presente articolo è una versione allargata della omonima conferenza tenuta a Milano durante il XVII convegno nazionale UMI nel settembre 2003. L'articolo ha come abiettivo principale quello di presentare una introduzione, il più possibile elementare, ai problemi di razionalità/unirazionalità in geometria algebrica. Avendo come punto di riferimento l'esempio delle ipersuperfici dello spazio proiettivo complesso, in particolare le ipersuperfici cubiche, vengono presentati temi classici e problemi...
Projective embeddings of toric varieties
Projective homogeneous varieties birational to quadrics.
Projektive Einbettung komplexer Mannigfaltigkeiten.
Properties of -p . p for Gorenstein surface singularities.
Punctual Hilbert schemes and resolutions of multiple point singularities.
Quadratic forms and singularities of genus one or two
We study singularities obtained by the contraction of the maximal divisor in compact (non-kählerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be -Gorenstein, numerically Gorenstein or Gorenstein. A family of polynomials depending on the configuration of the curves computes the discriminants of the quadratic forms of these singularities. We introduce a multiplicative branch topological invariant which determines the twisting coefficient of a non-vanishing...
Quadro-quadric Cremona transformations in low dimensions via the -correspondence
It has been previously established that a Cremona transformation of bidegree (2,2) is linearly equivalent to the projectivization of the inverse map of a rank 3 Jordan algebra. We call this result the “-correspondence”. In this article, we apply it to the study of quadro-quadric Cremona transformations in low-dimensional projective spaces. In particular we describe new very simple families of such birational maps and obtain complete and explicit classifications in dimension 4 and 5.
Quasi-Gorenstein Fano 3-folds with isolated non-rational loci
Quasihomogeneous Singularities.
Quasi-lines and their degenerations
In this paper we study the structure of manifolds that contain a quasi-line and give some evidence towards the fact that the irreducible components of degenerations of the quasi-line should determine the Mori cone. We show that the minimality with respect to a quasi-line yields strong restrictions on fibre space structures of the manifold.
Quelques plongements projectifs non speciaux de surfaces rationnelles.
Quelques propriétés des transformations birationnelles du plan projectif complexe, une histoire pour S.
On présente certaines (malheureusement pas toutes) propriétés connues du groupe de Cremona en faisant, lorsque c’est possible, un parallèle avec le groupe des automorphismes polynomiaux de . Les propriétés abordées seront essentiellement de nature algébrique : théorème de génération, sous-groupes finis, sous-groupes de type fini, description du groupe d’automorphismes du groupe de Cremona,... mais aussi de nature dynamique : classification des transformations birationnelles, centralisateur, dynamique...
Quelques revetements définis sur Q.
Raggi estremali di varietà proiettive lisce
Ramification dans le corps des modules
Soit un revêtement de la droite projective défini sur , de groupe de monodromie . Soit le compositum des corps de rationalité des points de branchement , et le corps des modules correspondants. Partant du lien entre corps des modules et espaces de Hurwitz, on étudie la géométrie et l’arithmétique de ces espaces et des espaces de configuration de points complétés pour évaluer la ramification dans des mauvaises places de qui ne divisent pas l’ordre de , mais où les points de branchements...