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) Georg Schumacher - Marburf,
Titre The Weil-Petersson current for moduli of vector bundles and applications to orbifolds
Horaire14:00 à 15:00
RésumeWe investigate stable holomorphic vector bundles on a compact complex Kähler manifold and more generally on an orbifold that is equipped with a Kähler structure. We use the existence of Hermite-Einstein connections in this set-up and construct a generalized Weil-Petersson form on the moduli space of stable vector bundles with fixed determinant bundle. We show that the Weil-Petersson form extends as a (semi-)positive closed current for degenerating families that are restrictions of coherent sheaves. Such an extension will be called a Weil-Petersson current. When the orbifold is of Hodge type, there exists a determinant line bundle on the moduli space; this line bundle carries a Quillen metric, whose curvature coincides with the generalized Weil-Petersson form. As an application we show that the determinant line bundle extends to a suitable compactification of the moduli space.