Higher dimensional polarized varieties with non-integral nefvalue.
Higher order differentials and Weierstrass points on Gorenstein curves.
Hyperelliptic surfaces of general type with K2 > 4x.
Improvement of Grauert-Riemenschneider's theorem for a normal surface
Let be a desingularization of a normal surface . The group Pic is provided with an order relation , defined by . for any effective exceptional divisor . Comparing to the usual order relation we define the ceiling of which is an exceptional divisor. This notion allows us to improve the usual vanishing theorem and we deduce from it a numerical criterion for rationality and a genus formula for a curve on a normal surface; the difficulty lies in the case of a Weil divisor which is not a Cartier...
Intersection-theoretical computations on
In this paper we explore several concrete problems, all more or less related to the intersection theory of the moduli space of (stable) curves, introduced by Mumford [Mu 1].
Invariante Divisoren und Schnitthomologie von torischen Varietäten
In this article, we complete the interpretation of groups of classes of invariant divisors on a complex toric variety X of dimension n in terms of suitable (co-) homology groups. In [BBFK], we proved the following result (see Satz 1 below): Let and denote the groups of classes of invariant Cartier resp. Weil divisors on X. If X is non degenerate (i.e., not equivariantly isomorphic to the product of a toric variety and a torus of positive dimension), then the natural homomorphisms and are...
Irreducibility and monodromy of some families of linear series
Irreducibility of some families of linear series with Brill-Noether number. I
Killing divisor classes by algebraisation
It is proved that any isolated singularity of complete intersection has an algebraisation whose divisor class group is finitely generated.
La variété de Picard d'une variété complète
Le théorème de Brill-Noether
Length of Extremal Rays and Generalized Adjunction.
Les fibrés de rang deux sur et leurs sections
L'existence de certaines spécialisations de courbes projective
Limit linear series: Basic theory.
Line bundles on toroidal groups.
Line bundles with partially vanishing cohomology
Define a line bundle on a projective variety to be -ample, for a natural number , if tensoring with high powers of kills coherent sheaf cohomology above dimension . Thus 0-ampleness is the usual notion of ampleness. We show that -ampleness of a line bundle on a projective variety in characteristic zero is equivalent to the vanishing of an explicit finite list of cohomology groups. It follows that -ampleness is a Zariski open condition, which is not clear from the definition.
Linear Systems on Projective Spaces.
Linear systems on quasi-abelian varieties.
Linear systems representing threefolds which are scrolls on a rational surface.