Annals of Global Analysis and Geometry

, Volume 56, Issue 3, pp 583–596 | Cite as

The Simanca metric admits a regular quantization

  • Francesco Cannas Aghedu
  • Andrea LoiEmail author


Let \(g_\mathrm{{S}}\) be the Simanca metric on the blow-up \(\tilde{\mathbb {C}}^2\) of \({\mathbb {C}}^2\) at the origin. We show that \((\tilde{\mathbb {C}}^2,g_\mathrm{{S}})\) admits a regular quantization. We use this fact to prove that all coefficients in the Tian–Yau–Zelditch expansion for the Simanca metric vanish and that a dense subset of \((\tilde{\mathbb {C}}^2, g_\mathrm{{S}})\) admits a Berezin quantization.


Kähler manifolds TYZ asymptotic expansion Radial metrics Scalar flat metrics Projectively induced metrics Simanca metric Berezin quantization 

Mathematics Subject Classification

53C55 58C25 58F06 



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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di CagliariCagliariItaly

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