归一化体积函数极小值的唯一性

IF 1.8 2区 数学 Q1 MATHEMATICS
Chenyang Xu, Ziquan Zhuang
{"title":"归一化体积函数极小值的唯一性","authors":"Chenyang Xu, Ziquan Zhuang","doi":"10.4310/cjm.2021.v9.n1.a2","DOIUrl":null,"url":null,"abstract":"We confirm a conjecture of Chi Li which says that the minimizer of the normalized volume function for a klt singularity is unique up to rescaling. This is achieved by defining stability thresholds for valuations, and then showing that a valuation is a minimizer if and only if it is K-semistable, and that K-semistable valuation is unique up to rescaling. As applications, we prove a finite degree formula for volumes of klt singularities and an effective bound of the local fundamental group of a klt singularity.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2020-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"30","resultStr":"{\"title\":\"Uniqueness of the minimizer of the normalized volume function\",\"authors\":\"Chenyang Xu, Ziquan Zhuang\",\"doi\":\"10.4310/cjm.2021.v9.n1.a2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We confirm a conjecture of Chi Li which says that the minimizer of the normalized volume function for a klt singularity is unique up to rescaling. This is achieved by defining stability thresholds for valuations, and then showing that a valuation is a minimizer if and only if it is K-semistable, and that K-semistable valuation is unique up to rescaling. As applications, we prove a finite degree formula for volumes of klt singularities and an effective bound of the local fundamental group of a klt singularity.\",\"PeriodicalId\":48573,\"journal\":{\"name\":\"Cambridge Journal of Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2020-05-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"30\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cambridge Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/cjm.2021.v9.n1.a2\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cambridge Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cjm.2021.v9.n1.a2","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 30

摘要

我们证实了池莉的一个猜想,即klt奇异性的归一化体积函数的极小值在重新缩放之前是唯一的。这是通过定义估值的稳定性阈值来实现的,然后证明估值是极小值,当且仅当它是K-半稳定的,并且K-半稳定性估值在重新缩放之前是唯一的。作为应用,我们证明了klt奇点体积的有限度公式和klt奇点的局部基群的有效界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Uniqueness of the minimizer of the normalized volume function
We confirm a conjecture of Chi Li which says that the minimizer of the normalized volume function for a klt singularity is unique up to rescaling. This is achieved by defining stability thresholds for valuations, and then showing that a valuation is a minimizer if and only if it is K-semistable, and that K-semistable valuation is unique up to rescaling. As applications, we prove a finite degree formula for volumes of klt singularities and an effective bound of the local fundamental group of a klt singularity.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
3.10
自引率
0.00%
发文量
7
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信