On the discriminant locus of an ample and spanned line bundle.
On the discriminant variety of a projective manifold.
On the Griffiths group of the cubic sevenfold.
On the l-adic cohomology of Siegel threefolds.
On the nonemptiness of the adjoint linear system of a hyperplane section of a threefold.
On the non-existence of Kähler structures on certain closed and oriented differentiable 6-manifolds.
Orbifolds, special varieties and classification theory
This article gives a description, by means of functorial intrinsic fibrations, of the geometric structure (and conjecturally also of the Kobayashi pseudometric, as well as of the arithmetic in the projective case) of compact Kähler manifolds. We first define special manifolds as being the compact Kähler manifolds with no meromorphic map onto an orbifold of general type, the orbifold structure on the base being given by the divisor of multiple fibres. We next show that rationally connected Kähler...
Orbifolds, special varieties and classification theory: an appendix
For any compact Kähler manifold and for any equivalence relation generated by a symmetric binary relation with compact analytic graph in , the existence of a meromorphic quotient is known from Inv. Math. 63 (1981). We give here a simplified and detailed proof of the existence of such quotients, following the approach of that paper. These quotients are used in one of the two constructions of the core of given in the previous paper of this fascicule, as well as in many other questions.
Primitive Line Bundles on Abelian Threefolds.
Projective 7-folds with positive defect
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.
Scrolls and quartics.
Shafarevich maps and plurigenera of algebraic varieties.
Smooth double subvarieties on singular varieties, III
Let k be an algebraically closed field, char k = 0. Let C be an irreducible nonsingular curve such that rC = S ∩ F, r ∈ ℕ, where S and F are two surfaces and all the singularities of F are of the form , s ∈ ℕ. We prove that C can never pass through such kind of singularities of a surface, unless r = 3a, a ∈ ℕ. We study multiplicity-r structures on varieties r ∈ ℕ. Let Z be a reduced irreducible nonsingular (n-1)-dimensional variety such that rZ = X ∩ F, where X is a normal n-fold, F is a (N-1)-fold...
Some geometry and combinatorics for the -invariant of ternary cubics.
Some intrinsic and extrinsic characterizations of the projective space
Some Remarks About Reider's Article 'On the Infinitesimal Torelli Theorem for Certain Irregular Surfaces of General Type'.
Sur des variétés de Moishezon dont le groupe de Picard est de rang un
Sur les variétés telles que par points passe une courbe de de degré donné
Soit , , et des entiers. On introduit la classe des sous-variétés de dimension d’un espace projectif, telles que pour générique, il existe une courbe rationnelle normale de degré , contenue dans et passant par les points ; engendre un espace projectif dont la dimension, pour , et donnés, est la plus grande possible compte tenu de la première propriété. Sous l’hypothèse , on détermine toutes les variétés appartenant à la classe . On montre en particulier qu’il existe une...
Threefolds of non negative Kodaira dimension with sectional genus less than or equal to 15