@article{578e322333b04e3089459047aab5903e,
title = "OPENNESS OF K-SEMISTABILITY FOR FANO VARIETIES",
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.",
author = "Harold Blum and Yuchen Liu and Chenyang Xu",
note = "Funding Information: H.B. was partially supported by National Science Foundation (NSF) grant DMS-1803102. Y.L. was partially supported by the Della Pietra Endowed Postdoctoral Fellowship of the MSRI (NSF grant DMS-1440140). C.X. was partially supported by a Chern Professorship of the MSRI (NSF grant DMS-1440140) and NSF grants DMS-1901849 and DMS-1952531. Publisher Copyright: {\textcopyright} 2022 Duke University Press. All rights reserved.",
year = "2022",
doi = "10.1215/00127094-2022-0054",
language = "English (US)",
volume = "171",
pages = "2753--2797",
journal = "Duke Mathematical Journal",
issn = "0012-7094",
publisher = "Duke University Press",
number = "13",
}