La correspondance de Langlands sur les corps de fonctions
La stabilité de la restriction à une courbe lisse d'un fibré de rang 2 sur une surface algébrique.
Lagrangian fibrations on generalized Kummer varieties
We investigate the existence of Lagrangian fibrations on the generalized Kummer varieties of Beauville. For a principally polarized abelian surface of Picard number one we find the following: The Kummer variety is birationally equivalent to another irreducible symplectic variety admitting a Lagrangian fibration, if and only if is a perfect square. And this is the case if and only if carries a divisor with vanishing Beauville-Bogomolov square.
Lagrangian subvarieties of the moduli space of stable vector bundles on a regular algebraic surface with pg > 0.
Lemme fondamental et endoscopie, une approche géométrique
Le “principe de fonctorialité”, conjecturé par Langlands à la fin des années 60, est un moyen remarquablement synthétique d’unifier et exprimer certains liens profonds entre formes automorphes, arithmétique et géométrie algébrique. Son apparente simplicité contraste fortement avec la difficulté des techniques utilisées pour l’aborder. Parmi celles-ci, la stabilisation de la formule des traces d’Arthur–Selberg bute depuis 25 ans sur une conjecture d’analyse harmonique sur des groupes -adiques :...
Local and global theory of the moduli of polarized Calabi-Yau manifolds.
In this paper we review the moduli theory of polarized CY manifolds. We briefly sketched Kodaira-Spencer-Kuranishi local deformation theory developed by the author and G. Tian. We also construct the Teichmüller space of polarized CY manifolds following the ideas of I. R. Shafarevich and I. I. Piatetski-Shapiro. We review the fundamental result of E. Viehweg about the existence of the course moduli space of polarized CY manifolds as a quasi-projective variety. Recently S. Donaldson computed the moment...
Local degeneration of the moduli space of vector bundles and factorization of rank two theta functions. I.
Local Structure of Brill-Noether Strata in the Moduli Space of Flat Stable Bundles
Local structure of the moduli space of vector bundles over curves.
Logarithmic geometry and algebraic stacks
L'unirazionalità della varietà dei moduli delle curve di genere dodici