Extending extremal contractions from an ample section.
Extension of maps defined on many fibres.
Let S be a fibred surface. We prove that the existence of morphisms from non countably many fibres to curves implies, up to base change, the existence of a rational map from S to another surface fibred over the same base reflecting the properties of the original morphisms. Under some conditions of unicity base change is not needed and one recovers exactly the initial maps.
Extensions of vector bundles and rationality of certain moduli spaces of stable bundles.
Extremal contractions from 4-dimensional manifolds to 3-folds
Extremal rational elliptic surfaces in characteristic p. I. Beauville surfaces.
Extremal rays on higher dimensional projective varieties.
Extremal rays on smooth threefolds
Factorization of a Birational Morphism Between 4-Folds*.
Faisceaux de Darboux et questions connexes dans l'espace affine courbe
Famiglie di curve nodali su superfici proiettive
Famiglie di curve sulle superfici algebriche
Families of algebraic curves with nodes
Families of Arcs on rational surface singularities.
Families of Curves on Surfaces.
Families of Curves with Nodes on K-3 Surfaces.
Families of hypersurfaces of large degree
Grauert and Manin showed that a non-isotrivial family of compact complex hyperbolic curves has finitely many sections. We consider a generic moving enough family of high enough degree hypersurfaces in a complex projective space. We show the existence of a strict closed subset of its total space that contains the image of all its sections.
Families of quintic surfaces and curves
Families of smooth curves on surface singularities and wedges
Following the study of the arc structure of singularities, initiated by J. Nash, we give criteria for the existence of smooth curves on a surface singularity (S,O) and of smooth branches of its generic hypersurface section. The main applications are the following: the existence of a natural partition of the set of smooth curves on (S,O) into families, a description of each of them by means of chains of infinitely near points and their associated maximal cycle and the existence of smooth curves on...
Families of supersingular abelian surfaces
Fano bundles of rank 2 on surfaces