Moment Maps, Scalar Curvature and Quantization of Kähler Manifolds

Abstract

Building on Donaldson’s work on constant scalar curvature metrics, we study the space of regular Kähler metrics E_ω, i.e. those for which deformation quantization has been defined by Cahen, Gutt and Rawnsley. After giving, in Sects. 2 and 3 a review of Donaldson’s moment map approach, we study the ‘‘essential’’ uniqueness of balanced basis (i.e. of coherent states) in a more general setting (Theorem 2.5). We then study the space E_ω in Sect.4 and we show in Sect.5 how all the tools needed can be defined also in the case of non-compact manifolds.