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1 September 2020 Birational superrigidity and K-stability of Fano complete intersections of index 1
Ziquan Zhuang
Duke Math. J. 169(12): 2205-2229 (1 September 2020). DOI: 10.1215/00127094-2020-0010

Abstract

We prove that every smooth Fano complete intersection of index 1 and codimension r in P n + r is birationally superrigid and K-stable if n 10 r . We also propose a generalization of Tian’s criterion of K-stability and, as an application, prove the K-stability of the complete intersection of a quadric and a cubic in P 5 . In the appendix (written jointly with C. Stibitz), we prove the conditional birational superrigidity of Fano complete intersections of higher index in large dimension.

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Ziquan Zhuang. "Birational superrigidity and K-stability of Fano complete intersections of index 1 ." Duke Math. J. 169 (12) 2205 - 2229, 1 September 2020. https://doi.org/10.1215/00127094-2020-0010

Information

Received: 5 April 2019; Revised: 2 January 2020; Published: 1 September 2020
First available in Project Euclid: 3 June 2020

MathSciNet: MR4139041
Digital Object Identifier: 10.1215/00127094-2020-0010

Subjects:
Primary: 14J45
Secondary: 14C20, 14E08, 14M10, 32Q20

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 12 • 1 September 2020
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