{"title":"光滑kähler-Einstein范诺流形模空间的拟投影性","authors":"Chi Li, Chi Li, Xiaowei Wang, Chenyang Xu","doi":"10.24033/ASENS.2365","DOIUrl":null,"url":null,"abstract":"In this note, we prove that there is a canonical continuous Hermitian metric on the CM line bundle over the proper moduli space M of smoothable Kahler-Einstein Fano varieties. The curvature of this metric is the Weil-Petersson current, which exists as a positive (1,1)-current on M and extends the canonical Weil-Petersson current on the moduli space parametrizing smooth Kahler-Einstein Fano manifoldsM. As a consequence, we show that the CM line bundle is nef and big on M and its restriction on M is ample.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"46 1","pages":"739-772"},"PeriodicalIF":1.3000,"publicationDate":"2018-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Quasi-projectivity of the moduli space of smooth kähler-Einstein fano manifolds\",\"authors\":\"Chi Li, Chi Li, Xiaowei Wang, Chenyang Xu\",\"doi\":\"10.24033/ASENS.2365\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note, we prove that there is a canonical continuous Hermitian metric on the CM line bundle over the proper moduli space M of smoothable Kahler-Einstein Fano varieties. The curvature of this metric is the Weil-Petersson current, which exists as a positive (1,1)-current on M and extends the canonical Weil-Petersson current on the moduli space parametrizing smooth Kahler-Einstein Fano manifoldsM. As a consequence, we show that the CM line bundle is nef and big on M and its restriction on M is ample.\",\"PeriodicalId\":50971,\"journal\":{\"name\":\"Annales Scientifiques De L Ecole Normale Superieure\",\"volume\":\"46 1\",\"pages\":\"739-772\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2018-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Scientifiques De L Ecole Normale Superieure\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.24033/ASENS.2365\",\"RegionNum\":1,\"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":"Annales Scientifiques De L Ecole Normale Superieure","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.24033/ASENS.2365","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Quasi-projectivity of the moduli space of smooth kähler-Einstein fano manifolds
In this note, we prove that there is a canonical continuous Hermitian metric on the CM line bundle over the proper moduli space M of smoothable Kahler-Einstein Fano varieties. The curvature of this metric is the Weil-Petersson current, which exists as a positive (1,1)-current on M and extends the canonical Weil-Petersson current on the moduli space parametrizing smooth Kahler-Einstein Fano manifoldsM. As a consequence, we show that the CM line bundle is nef and big on M and its restriction on M is ample.
期刊介绍：
The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics.
Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition.
The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.
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