Sorbonne Université CNRS Paris Diderot

Séminaire d’Analyse et Géométrie

Scalar curvature and an infinite dimensional hyperkähler reduction

Jacopo Stoppa - SISSA, Trieste

mardi 19 février 2019 à 14:00
Barre 15-25, 5ème étage, salle 02

Donaldson 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.

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