{"title":"Quot-scheme limit of Fubini-Study metrics and Donaldson's functional for\n vector bundles","authors":"Y. Hashimoto, Julien Keller","doi":"10.46298/epiga.2022.6577","DOIUrl":null,"url":null,"abstract":"For a holomorphic vector bundle $E$ over a polarised K\\\"ahler manifold, we\nestablish a direct link between the slope stability of $E$ and the asymptotic\nbehaviour of Donaldson's functional, by defining the Quot-scheme limit of\nFubini-Study metrics. In particular, we provide an explicit estimate which\nproves that Donaldson's functional is coercive on the set of Fubini-Study\nmetrics if $E$ is slope stable, and give a new proof of Hermitian-Einstein\nmetrics implying slope stability.","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2018-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Epijournal de Geometrie Algebrique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/epiga.2022.6577","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
For a holomorphic vector bundle $E$ over a polarised K\"ahler manifold, we
establish a direct link between the slope stability of $E$ and the asymptotic
behaviour of Donaldson's functional, by defining the Quot-scheme limit of
Fubini-Study metrics. In particular, we provide an explicit estimate which
proves that Donaldson's functional is coercive on the set of Fubini-Study
metrics if $E$ is slope stable, and give a new proof of Hermitian-Einstein
metrics implying slope stability.