A note on moment maps and Kahler-Einstein manifolds

摘要

We collect some properties of the moment map relative to the isometric and holomorphic action of a compact Lie group G on a (compact) Kahler (Einstein) manifold; in particular, we study some invariants which only depend on the cohomology class of the invariant Kahler form and then specialize to the complex projective space when the group G is simple and acts linearly.