GEOMETRIC QUANTIZATION OF COUPLED KÄHLER-EINSTEIN METRICS

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Abstract

We study the quantization of coupled Kähler-Einstein (CKE) metrics, namely we approximate CKE metrics by means of the canonical Bergman metrics, called “balanced metrics”. We prove the existence and weak convergence of balanced metrics for the negative first Chern class, while for the positive first Chern class, we introduce an algebrogeometric obstruction which interpolates between the Donaldson-Futaki invariant and Chow weight. Then we show the existence and weak convergence of balanced metrics on CKE manifolds under the vanishing of this obstruction. Moreover, restricted to the case when the automorphism group is discrete, we also discuss approximate solutions and a gradient flow method towards the smooth convergence.

Original languageEnglish
Pages (from-to)1817-1849
Number of pages33
JournalAnalysis and PDE
Volume14
Issue number6
DOIs
Publication statusPublished - 2021

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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