abstract: In these talks I will discuss a class of torus actions on Kahler manifolds which generalize toric actions to torus actions of higher codimension. A classification of a large class of compact manifolds admitting such actions is obtained.
This is joint work with Vestislav Apostolov, Paul Gauduchon and Christina Tonnesen Friedman, and appears in section 2 of Hamiltonian 2-forms in Kahler geometry II.