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arXiv · 1508.02643

Quantisation of extremal Kähler metrics

Yoshinori Hashimoto
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Abstract

Suppose that a polarised Kähler manifold $(X,L)$ admits an extremal metric $ω$. We prove that there exists a sequence of Kähler metrics $\{ ω_k \}_k$, converging to $ω$ as $k \to \infty$, each of which satisfies the equation $\bar{\partial} \text{grad}^{1,0}_{ω_k} ρ_k (ω_k)=0$; the $(1,0)$-part of the gradient of the Bergman function is a holomorphic vector field.

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BibTeXRIS

Yoshinori Hashimoto. 2017-06-01. Quantisation of extremal Kähler metrics. https://doi.org/10.1007/s12220-020-00381-7

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