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July, 2019 Relative stability associated to quantised extremal Kähler metrics
Yoshinori HASHIMOTO
J. Math. Soc. Japan 71(3): 861-880 (July, 2019). DOI: 10.2969/jmsj/79947994

Abstract

We study algebro-geometric consequences of the quantised extremal Kähler metrics, introduced in the previous work of the author. We prove that the existence of quantised extremal metrics implies weak relative Chow polystability. As a consequence, we obtain asymptotic weak relative Chow polystability and relative $K$-semistability of extremal manifolds by using quantised extremal metrics; this gives an alternative proof of the results of Mabuchi and Stoppa–Székelyhidi. In proving them, we further provide an explicit local density formula for the equivariant Riemann–Roch theorem.

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Yoshinori HASHIMOTO. "Relative stability associated to quantised extremal Kähler metrics." J. Math. Soc. Japan 71 (3) 861 - 880, July, 2019. https://doi.org/10.2969/jmsj/79947994

Information

Received: 23 February 2018; Published: July, 2019
First available in Project Euclid: 25 April 2019

zbMATH: 07121556
MathSciNet: MR3984245
Digital Object Identifier: 10.2969/jmsj/79947994

Subjects:
Primary: 32Q26
Secondary: 53C55

Keywords: extremal Kähler metrics , relative $K$-stability , relative weak Chow stability

Rights: Copyright © 2019 Mathematical Society of Japan

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Vol.71 • No. 3 • July, 2019
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