Fibrés uniformes de rang 5 sur
Fibrés uniformes de rang élevé sur
Un fibré vectoriel holomorphe sur est dit uniforme si ses images réciproques sous tous les plongements linéaires sont isomorphes. Nous classons les fibrés uniformes de rang 4 sur .
Fibrés uniformes de type sur
Dans cet article, on donne un début de classification des fibrés vectoriels algébriques uniformes de type de décomposition sur . Les seuls tels fibrés de rang 4 sont les fibrés “évidents” et sont donc homogènes. Enfin, on montre qu’un fibré vectoriel uniforme de type sur est stable si et seulement si ce fibré et son dual n’ont pas de sections globales non triviales.
Fibrés vectoriels de rang 1 d'ordre fini
Fibrés vectoriels semi-stables sur une courbe de Mumford.
Fibrés vectoriels spéciaux
Fibrés vectoriels topologiques de rang élevé sur une hypersurface
Flat modules in algebraic geometry
Flat vector bundles and the fundamental group in non-zero characteristics
Fourier Mukai transforms and applications to string theory.
El artículo es una introducción a la transformación de Fourier-Mukai y sus aplicaciones a varios problemas de móduli, teoría de cuerdas y simetría "mirror". Se desarrollan los fundamentos necesarios para las transformaciones de Fourier-Mukai, entre ellos las categorías derivadas y los functores integrales. Se explican además sus versiones relativas, que se necesitan para precisar la noción de T-dualidad fibrada en variedades de Calabi-Yau elípticas de dimensión tres. Se consideran también varias...
Fourier-Mukai transform and index theory.
Fourier-Mukai transforms and stable bundles on elliptic curves.
Fragmented deformations of primitive multiple curves
A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y that can be locally embedded in a smooth surface, and such that Y red is smooth. We study the deformations of Y to curves with smooth irreducible components, when the number of components is maximal (it is then the multiplicity n of Y). We are particularly interested in deformations to n disjoint smooth irreducible components, which are called fragmented deformations. We describe them completely. We give also a characterization...
Free pencils on divisors.
Freeness of hyperplane arrangements and related topics
These are the expanded notes of the lecture by the author in “Arrangements in Pyrénées”, June 2012. We are discussing relations of freeness and splitting problems of vector bundles, several techniques proving freeness of hyperplane arrangements, K. Saito’s theory of primitive derivations for Coxeter arrangements, their application to combinatorial problems and related conjectures.
Frobenius pull-back of vector bundles of rank 2 over non-uniruled varieties.
Gaps in Chern Classes of Rank 2 Stable Reflexive Sheaves.
Gauss-Manin stratification and stratified fundamental group schemes
We define the zero-th Gauss-Manin stratification of a stratified bundle with respect to a smooth morphism and use it to study the homotopy sequence of stratified fundamental group schemes.
General stable bundles arising as normal bundles of projective curves.
Generalized Fourier-Mukai transforms.