Présentation
La rencontre sera constituée de 3 mini-cours et de 4 exposés de recherche.
Mini-cours
- Benoît Claudon : Topology of klt singularities.
- Tomas Krämer : Holonomic D-modules on abelian varieties.
- Claude Sabbah : Irregular Hodge theory and periods
Exposés
- Rodolfo Aguilar Aguilar : Arrangements, fundamental groups and homology planes
Résumé : We will show some examples of homology planes: smooth, affine complex surfaces with trivial reduced integral homology, of log-general type which have infinite fundamental group. These could be the first examples where such infinitude is shown. They arise as partial compactifications of the complement of an arrangement of lines in the complex projective plane. The infinitude follows from quotients to infinite fundamental groups of orbicurves induced by orbifolds fibrations.
- Katia Amerik : Parabolic automorphisms of hyperkähler manifolds
Résumé : As observed by Serge Cantat, an automorphism of a K3 surface which is a fiberwise translation in an elliptic pencil, acts with dense orbits in the fibers; as a consequence, if a K3 surface has two such automorphisms (with distinct pencils), then the group they generate acts ergodically. We show that the same holds for arbitrary hyperkähler manifolds, as an application of Deligne semisimplicity theorem. This is a joint work with Misha Verbitsky.
- Olivier Benoist : On the problem of generating Chow groups by smooth subvarieties
Résumé : An old question of Borel and Haefliger asks whether the Chow groups of a smooth projective variety are generated by smooth subvarieties. Despite positive results of Hironaka and Kleiman in particular cases, the answer was found to be negative by Hartshorne, Rees and Thomas. We will consider this question, as well as variants of it in real algebraic geometry, and we will present new positive results (using linkage theory) and new negative results (using divisibility properties of Chern numbers).
- Henri Guenancia : Numerical characterization of complex tori quotients
Résumé : I will report on a recent joint work with Benoît Claudon and Patrick Graf. We give a numerical criterion to characterize among compact Kähler spaces with klt singularities the quotients T/G of a complex torus T by a finite group G acting freely in codimension two. The main ingredients in the proof are the Beauville-Bogomolov decomposition theorem for singular Kähler spaces with zero first Chern class and a singular version of Bogomolov-Gieseker inequality for stable reflexive sheaves.
Bonnes adresses
Pour se restaurer, voici un lien avec quelques trattorias (merci Bruno !).
Organisateurs
Benoît Claudon, Philippe Eyssidieux et Bruno Klingler
