Quantization of symplectic fibrations and canonical metrics

Louis Ioos, Leonid Polterovich

Research output: Contribution to journalArticlepeer-review

Abstract

We relate Berezin-Toeplitz quantization of higher rank vector bundles to quantum-classical hybrid systems and quantization in stages of symplectic fibrations. We apply this picture to the analysis and geometry of vector bundles, including the spectral gap of the Berezin transform and the convergence rate of Donaldson's iterations toward balanced metrics on stable vector bundles. We also establish refined estimates in the scalar case to compute the rate of Donaldson's iterations toward balanced metrics on Kähler manifolds with constant scalar curvature.

Original languageEnglish
Article number2350043
JournalInternational Journal of Mathematics
Volume34
Issue number8
DOIs
StatePublished - 1 Jul 2023

Keywords

  • Bergman kernel
  • Geometric quantization
  • canonical Kähler metrics
  • symplectic fibrations

All Science Journal Classification (ASJC) codes

  • General Mathematics

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