Séminaires : Séminaire d'Analyse et Géométrie

Equipe(s) :
Responsables :O. Biquard, A. Deruelle, I. Itenberg, X. Ma
Email des responsables : {olivier.biquard, alix.deruelle, ilia.itenberg, xiaonan.ma}@imj-prg.fr
Salle : 15–25.502
Adresse :Jussieu

Orateur(s) Valentino Tosatti - Northwestern University et IHP,
Titre Smooth collapsing of Ricci-flat metrics
Horaire14:00 à 15:00
RésumeConsider a compact Calabi-Yau manifold with a holomorphic fibration onto a lower-dimensional space, and consider a family of Ricci-flat Kahler metrics on the total space whose Kahler class is degenerating to the pullback of a class from the base. In earlier work I proved that the metric collapse, away from the singular fibers, to a limiting metric on the base, in the locally uniform topology (and smoothly if the fibers are tori). I will describe new estimates that prove a uniform Holder bound in general, and bounds for all derivatives when the smooth fibers are isomorphic to each other.