Remarks on asymptotic isometric embeddings of conic transforms for torus actions (Q6645830)

In this paper, the author focuses on the asymptotics of the Szegő kernel along rays in the weight space. Consider a Hodge manifold and assume that a torus acts on it in a Hamiltonian and holomorphic manner and that this action linearizes on a given quantizing line bundle. Inside the dual of the line bundle one can define the circle bundle, which is a strictly pseudoconvex CR manifold. Then, there is an associated unitary representation on the Hardy space of the circle bundle. Under suitable assumptions on the moment map, the author considers certain loci in the unit circle bundle, naturally associated to a ray through an irreducible weight. Their quotients are called conic transforms. He introduces maps which are asymptotic embeddings of conic transforms making use of the corresponding equivariant Szegő projector. \N\NThis paper is organized as follows: Section 1 is an introduction to the subject. Section 2 deals with motivations and preliminaries. The author recalls some basic definitions about orbifolds, conic transforms for torus actions and equivariant Szegő kernels. Section 3 is devoted to the proof of the main result.