Translator Disclaimer
15 September 2022 Openness of K-semistability for Fano varieties
Harold Blum, Yuchen Liu, Chenyang Xu
Author Affiliations +
Duke Math. J. 171(13): 2753-2797 (15 September 2022). DOI: 10.1215/00127094-2022-0054

Abstract

In this paper, we prove the openness of K-semistability in families of log Fano pairs by showing that the stability threshold is a constructible function on the fibers. We also prove that any special test configuration arises from a log canonical place of a bounded complement and establish properties of any minimizer of the stability threshold.

Citation

Download Citation

Harold Blum. Yuchen Liu. Chenyang Xu. "Openness of K-semistability for Fano varieties." Duke Math. J. 171 (13) 2753 - 2797, 15 September 2022. https://doi.org/10.1215/00127094-2022-0054

Information

Received: 6 February 2020; Revised: 12 October 2021; Published: 15 September 2022
First available in Project Euclid: 1 September 2022

Digital Object Identifier: 10.1215/00127094-2022-0054

Subjects:
Primary: 14J45
Secondary: 14E30

Keywords: Fano variety , K-stability , moduli spaces

Rights: Copyright © 2022 Duke University Press

JOURNAL ARTICLE
45 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.171 • No. 13 • 15 September 2022
Back to Top