A Hilbert-Mumford criterion for polystability in Kaehler geometry

Jeudi 9 octobre 2008 14:00-15:00 - Mundet i Riera Ignasi - Université de Barcelone

Résumé : Take a Kaehler manifold with a holomorphic action of a reductive group $G$.
Assume that the restriction of the action to a suitable maximal compact subgroup
$K\subset G$ is hamiltonian. We characterize the points whose G orbit meets the zero level set of the moment map in terms of a function defined on the visual boundary at infinity of G/K, which is an an analogue of the maximal weight function in GIT.
This allows to relate pointwise the symplectic quotient with the holomorphic (or GIT, in the projective case) quotient.

Lieu : bât. 425 - 121-123

A Hilbert-Mumford criterion for polystability in Kaehler geometry  Version PDF