Existence and deformations of Kähler–Einstein metrics on smoothable Q-Fano varieties

Cristiano Spotti; Song Sun; Chengjian Yao

doi:10.1215/00127094-3645330

Abstract

In this article we prove the existence of Kähler–Einstein metrics on $\mathbb{Q}$ -Gorenstein smoothable, K-polystable $\mathbb{Q}$ -Fano varieties, and we show how these metrics behave, in the Gromov–Hausdorff sense, under $\mathbb{Q}$ -Gorenstein smoothings.

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Cristiano Spotti. Song Sun. Chengjian Yao. "Existence and deformations of Kähler–Einstein metrics on smoothable $\mathbb{Q}$ -Fano varieties." Duke Math. J. 165 (16) 3043 - 3083, 1 November 2016. https://doi.org/10.1215/00127094-3645330

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Received: 29 December 2014; Revised: 27 October 2015; Published: 1 November 2016

First available in Project Euclid: 10 August 2016

zbMATH: 1362.53082

MathSciNet: MR3566198

Digital Object Identifier: 10.1215/00127094-3645330

Subjects:

Primary: 53C55

Secondary: 14J10 , 14J45 , 32J99 , 53C25

Keywords: compactification , Fano , Gromov–Hausdorff , Kahler–Einstein , K-stability , moduli , Monge–Ampère , separatedness

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