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) Jacopo Stoppa - SISSA, Trieste,
Titre Scalar curvature and an infinite dimensional hyperkähler reduction
Horaire14:00 à 15:00
RésumeDonaldson and Fujiki gave an interpretation of the constant scalar Kähler geometry (cscK equation) as an infinite-dimensional Kähler reduction. Donaldson and his student T. Hodge considered the problem of extending this naturally to a hyperkähler reduction and studied the resulting real and complex moment map equations in the special case of complex curves. I will discuss recent joint work with C. Scarpa (SISSA) in which we developed a different approach to this problem, based on general results of Biquard and Gauduchon. In particular we were able to write down the equations explicitly on complex surfaces and to solve them on some ruled surfaces for which the original cscK equation does not have solutions.