{"title":"K-SEMISTABILITY OF OPTIMAL DEGENERATIONS","authors":"Ruadhaí Dervan","doi":"10.1093/qmathj/haaa012","DOIUrl":null,"url":null,"abstract":"K-polystability of a polarized variety is an algebro-geometric notion conjecturally equivalent to the existence of a constant scalar curvature Kähler metric. When a variety is K-unstable, it is expected to admit a ‘most destabilizing’ degeneration. In this note we show that if such a degeneration exists, then the limiting scheme is itself relatively K-semistable.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":"71 1","pages":"989-995"},"PeriodicalIF":0.6000,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmathj/haaa012","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quarterly Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://ieeexplore.ieee.org/document/9434334/","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
K-polystability of a polarized variety is an algebro-geometric notion conjecturally equivalent to the existence of a constant scalar curvature Kähler metric. When a variety is K-unstable, it is expected to admit a ‘most destabilizing’ degeneration. In this note we show that if such a degeneration exists, then the limiting scheme is itself relatively K-semistable.
期刊介绍：
The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.
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