Geodesic rays in the space of Kahler metrics with T-symmetry

Let (M, omega, J) be a Kahler manifold, equipped with an effective Hamiltonian torus action rho : T -> Diff(M, omega, J) by isometries with moment map mu : M -> t*. We first construct a singular mixed polarization P-mix on M. Second we construct a one-parameter family of complex structures J(t) on Mwhich are compatible with omega. Furthermore the path of corresponding Kahler metrics g(t) is a complete geodesic ray in the space of Kahler metrics of M. Finally, we show that the corresponding family of Kahler polarizations P-t associated to J(t) converges to P-mix as t -> infinity. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.