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1 June 2019 On the proper moduli spaces of smoothable Kähler–Einstein Fano varieties
Chi Li, Xiaowei Wang, Chenyang Xu
Duke Math. J. 168(8): 1387-1459 (1 June 2019). DOI: 10.1215/00127094-2018-0069

Abstract

In this paper we investigate the geometry of the orbit space of the closure of the subscheme parameterizing smooth Kähler–Einstein Fano manifolds inside an appropriate Hilbert scheme. In particular, we prove that being K-semistable is a Zariski-open condition, and we establish the uniqueness of the Gromov–Hausdorff limit for a punctured flat family of Kähler–Einstein Fano manifolds. Based on these, we construct a proper scheme parameterizing the S-equivalent classes of Q-Gorenstein smoothable, K-semistable Q-Fano varieties, and we verify various necessary properties to guarantee that it is a good moduli space.

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Chi Li. Xiaowei Wang. Chenyang Xu. "On the proper moduli spaces of smoothable Kähler–Einstein Fano varieties." Duke Math. J. 168 (8) 1387 - 1459, 1 June 2019. https://doi.org/10.1215/00127094-2018-0069

Information

Received: 7 August 2017; Revised: 26 November 2018; Published: 1 June 2019
First available in Project Euclid: 3 May 2019

zbMATH: 07080115
MathSciNet: MR3959862
Digital Object Identifier: 10.1215/00127094-2018-0069

Subjects:
Primary: 14J45
Secondary: 14D20, 14J10, 53C25, 53C55

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 8 • 1 June 2019
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