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Moment Maps, Scalar Curvature and Quantization of Kähler Manifolds

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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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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Parma, Via D’Azeglio 85, Italy

    Claudio Arezzo

  2. Dipartimento di Matematica, Università di Cagliari, Via Ospedale 72, Italy

    Andrea Loi

Authors
  1. Claudio Arezzo
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  2. Andrea Loi
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Correspondence to Andrea Loi.

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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

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