Amphitheatre of Interdisciplinary Complex at the University of Lisbon

Miguel Abreu, Instituto Superior Técnico
Kahler metrics on toric orbifolds

In this talk I will describe how a symplectic approach to Kahler geometry on toric manifolds, presented in this seminar on July 2000, can be extended to the more general context of toric orbifolds. The main result is again an effective parametrization of all invariant Kahler metrics on a toric orbifold, via smooth functions on the corresponding moment polytope.

As an application I will give a simple explicit description of recent work of R. Bryant, producing interesting new families of extremal Kahler metrics. In particular, one obtains an extremal Kahler metric on any weighted projective space.