2008-02-01

Tim Goldberg, Cornell University

How to describe a moment polytope using a line bundle

Given a Hamiltonian group action, proving that a moment image is a convex polytope is sometimes much easier than figuring out exactly what the polytope is. But in certain cases, where the manifold is K\"ahler and admits a compatible holomorphic positive line bundle L, the sections of L can sometimes lead to descriptions of these moment polytopes. I will discuss several results about this, proved by M. Brion, V. Guillemin and R. Sjamaar, L. O'Shea and R. Sjamaar, P. Sch\"utzdeller, and myself.