{"title":"具有度和从下有界的不变量的Q-Fano变的有界性","authors":"Chen Jiang","doi":"10.24033/ASENS.2445","DOIUrl":null,"url":null,"abstract":"We show that $\\mathbb{Q}$-Fano varieties of fixed dimension with anti-canonical degrees and alpha-invariants bounded from below form a bounded family. As a corollary, K-semistable $\\mathbb{Q}$-Fano varieties of fixed dimension with anti-canonical degrees bounded from below form a bounded family.","PeriodicalId":50971,"journal":{"name":"Annales Scientifiques De L Ecole Normale Superieure","volume":"40 1","pages":"1235-1248"},"PeriodicalIF":1.3000,"publicationDate":"2017-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"49","resultStr":"{\"title\":\"Boundedness of Q-Fano varieties with degrees and alpha-invariants bounded from below\",\"authors\":\"Chen Jiang\",\"doi\":\"10.24033/ASENS.2445\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that $\\\\mathbb{Q}$-Fano varieties of fixed dimension with anti-canonical degrees and alpha-invariants bounded from below form a bounded family. As a corollary, K-semistable $\\\\mathbb{Q}$-Fano varieties of fixed dimension with anti-canonical degrees bounded from below form a bounded family.\",\"PeriodicalId\":50971,\"journal\":{\"name\":\"Annales Scientifiques De L Ecole Normale Superieure\",\"volume\":\"40 1\",\"pages\":\"1235-1248\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2017-05-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"49\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Scientifiques De L Ecole Normale Superieure\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.24033/ASENS.2445\",\"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.2445","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Boundedness of Q-Fano varieties with degrees and alpha-invariants bounded from below
We show that $\mathbb{Q}$-Fano varieties of fixed dimension with anti-canonical degrees and alpha-invariants bounded from below form a bounded family. As a corollary, K-semistable $\mathbb{Q}$-Fano varieties of fixed dimension with anti-canonical degrees bounded from below form a bounded family.
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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