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.
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Communicated by M.R. Douglas
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Arezzo, C., Loi, A. Moment Maps, Scalar Curvature and Quantization of Kähler Manifolds. Commun. Math. Phys. 246, 543–559 (2004). https://doi.org/10.1007/s00220-004-1053-3
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DOI: https://doi.org/10.1007/s00220-004-1053-3