K-stability for varieties with a big anticanonical class

Chenyang Xu

doi:10.46298/EPIGA.2023.10231

K-stability for varieties with a big anticanonical class

Chenyang Xu

Mathematics

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

4 Scopus citations

Abstract

We extend the algebraic K-stability theory to projective klt pairs with a big anticanonical class. While in general such a pair could behave pathologically, it is observed in this note that the K-semistability condition will force them to have a klt anticanonical model, whose stability property is the same as that of the original pair.

Original language	English (US)
Article number	7
Journal	Epijournal de Geometrie Algebrique
DOIs	https://doi.org/10.46298/EPIGA.2023.10231
State	Published - 2023

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

Keywords

K-stability
finite generation
log Fano varieties

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10.46298/EPIGA.2023.10231

Cite this

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title = "K-stability for varieties with a big anticanonical class",

abstract = "We extend the algebraic K-stability theory to projective klt pairs with a big anticanonical class. While in general such a pair could behave pathologically, it is observed in this note that the K-semistability condition will force them to have a klt anticanonical model, whose stability property is the same as that of the original pair.",

keywords = "K-stability, finite generation, log Fano varieties",

author = "Chenyang Xu",

year = "2023",

doi = "10.46298/EPIGA.2023.10231",

language = "English (US)",

journal = "Epijournal de Geometrie Algebrique",

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T1 - K-stability for varieties with a big anticanonical class

AU - Xu, Chenyang

PY - 2023

Y1 - 2023

N2 - We extend the algebraic K-stability theory to projective klt pairs with a big anticanonical class. While in general such a pair could behave pathologically, it is observed in this note that the K-semistability condition will force them to have a klt anticanonical model, whose stability property is the same as that of the original pair.

AB - We extend the algebraic K-stability theory to projective klt pairs with a big anticanonical class. While in general such a pair could behave pathologically, it is observed in this note that the K-semistability condition will force them to have a klt anticanonical model, whose stability property is the same as that of the original pair.

KW - K-stability

KW - finite generation

KW - log Fano varieties

UR - https://www.scopus.com/pages/publications/85175250621

UR - https://www.scopus.com/inward/citedby.url?scp=85175250621&partnerID=8YFLogxK

U2 - 10.46298/EPIGA.2023.10231

DO - 10.46298/EPIGA.2023.10231

M3 - Article

AN - SCOPUS:85175250621

SN - 2491-6765

JO - Epijournal de Geometrie Algebrique

JF - Epijournal de Geometrie Algebrique

M1 - 7

ER -

K-stability for varieties with a big anticanonical class

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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