Building on Donaldson's work on constant scalar curvature metrics, we study the space of regular Kaehler metrics {\cal E}_{\omega}, i.e. those for which deformation quantization has been defined by Cahen, Gutt and Rawnsley. After giving, in Section 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 \ref{mainteor}). We then study the space {\cal E}_{\omega} and we show how all the tools needed can be defined also in the case of non-compact manifolds.
Moment maps, scalar curvature and quantization of Kaehler manifolds
LOI, ANDREA;
2004-01-01
Abstract
Building on Donaldson's work on constant scalar curvature metrics, we study the space of regular Kaehler metrics {\cal E}_{\omega}, i.e. those for which deformation quantization has been defined by Cahen, Gutt and Rawnsley. After giving, in Section 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 \ref{mainteor}). We then study the space {\cal E}_{\omega} and we show how all the tools needed can be defined also in the case of non-compact manifolds.
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