GEOMETRIC QUANTIZATION OF COUPLED KÄHLER-EINSTEIN METRICS

研究成果: Contribution to journalArticle査読

抄録

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.

本文言語英語
ページ(範囲)1817-1849
ページ数33
ジャーナルAnalysis and PDE
14
6
DOI
出版ステータス出版済み - 2021

All Science Journal Classification (ASJC) codes

  • 分析
  • 数値解析
  • 応用数学

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