2018/02/15 by Andrea Galasso, Galasso, Andrea, Roberto Paoletti +1 · 1 citation
Mathematics · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.1802.05644
Let M be complex projective manifold, and A a positive line bundle on it. Assume that a compact and connected Lie group G acts on M in a Hamiltonian manner, and that this action linearizes to A. Then there is an associated unitary representation of G on the associated algebro-geometric Hardy space. If the moment map is nowhere vanishing, the isotypical component are all finite dimensional, they are generally not spaces of sections of some power of A. One is then led to study the local and global asymptotic properties the isotypical component associated to a weight k \boldsymbolν, when k→ +∞. In this paper, part of a series dedicated to this general theme, we consider the case G=U(2).