OPENNESS OF K-SEMISTABILITY FOR FANO VARIETIES

Harold Blum; Yuchen Liu; Chenyang Xu

doi:10.1215/00127094-2022-0054

OPENNESS OF K-SEMISTABILITY FOR FANO VARIETIES

Harold Blum, Yuchen Liu, Chenyang Xu

Mathematics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

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.

Original language	English (US)
Pages (from-to)	2753-2797
Number of pages	45
Journal	Duke Mathematical Journal
Volume	171
Issue number	13
DOIs	https://doi.org/10.1215/00127094-2022-0054
State	Published - 2022

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1215/00127094-2022-0054

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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",

year = "2022",

doi = "10.1215/00127094-2022-0054",

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AU - Liu, Yuchen

AU - Xu, Chenyang

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N2 - 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.

AB - 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.

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DO - 10.1215/00127094-2022-0054

M3 - Article

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SN - 0012-7094

VL - 171

SP - 2753

EP - 2797

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

IS - 13

ER -

OPENNESS OF K-SEMISTABILITY FOR FANO VARIETIES

Abstract

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