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November 2020 On positivity of the CM line bundle on K-moduli spaces
Chenyang Xu, Ziquan Zhuang
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Ann. of Math. (2) 192(3): 1005-1068 (November 2020). DOI: 10.4007/annals.2020.192.3.7

Abstract

In this paper, we consider the CM line bundle on the K-moduli space, i.e., the moduli space parametrizing K-polystable Fano varieties. We prove it is ample on any proper subspace parametrizing reduced uniformly K-stable Fano varieties that conjecturally should be the entire moduli space. As a corollary, we prove that the moduli space parametrizing smoothable K-polystable Fano varieties is projective.

During the course of proof, we develop a new invariant for filtrations that can be used to test various K-stability notions of Fano varieties.

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Chenyang Xu. Ziquan Zhuang. "On positivity of the CM line bundle on K-moduli spaces." Ann. of Math. (2) 192 (3) 1005 - 1068, November 2020. https://doi.org/10.4007/annals.2020.192.3.7

Information

Published: November 2020
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2020.192.3.7

Subjects:
Primary: 14D20 , 14E30 , 14J45

Keywords: CM line bundle , Fano varieties , K-moduli , K-stability , projectivity

Rights: Copyright © 2020 Department of Mathematics, Princeton University

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Vol.192 • No. 3 • November 2020
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