{"title":"Pluricomplex Green's functions and Fano manifolds","authors":"Nicholas McCleerey, Valentino Tosatti","doi":"10.46298/epiga.2019.volume3.4706","DOIUrl":null,"url":null,"abstract":"We show that if a Fano manifold does not admit Kahler-Einstein metrics then\nthe Kahler potentials along the continuity method subconverge to a function\nwith analytic singularities along a subvariety which solves the homogeneous\ncomplex Monge-Ampere equation on its complement, confirming an expectation of\nTian-Yau.\n\n Comment: EpiGA Volume 3 (2019), Article Nr. 9","PeriodicalId":41470,"journal":{"name":"Epijournal de Geometrie Algebrique","volume":"1 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2018-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Epijournal de Geometrie Algebrique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/epiga.2019.volume3.4706","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: 6
Abstract
We show that if a Fano manifold does not admit Kahler-Einstein metrics then
the Kahler potentials along the continuity method subconverge to a function
with analytic singularities along a subvariety which solves the homogeneous
complex Monge-Ampere equation on its complement, confirming an expectation of
Tian-Yau.
Comment: EpiGA Volume 3 (2019), Article Nr. 9
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