{"title":"皮卡二阶 K 稳定光滑法诺三褶","authors":"Ivan Cheltsov, Elena Denisova, Kento Fujita","doi":"10.1017/fms.2024.5","DOIUrl":null,"url":null,"abstract":"<p>We prove that all smooth Fano threefolds in the families <img mimesubtype=\"png\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319152445390-0178:S2050509424000057:S2050509424000057_inline1.png?pub-status=live\" type=\"\"> and <img mimesubtype=\"png\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319152445390-0178:S2050509424000057:S2050509424000057_inline2.png?pub-status=live\" type=\"\"> are K-stable, and we also prove that smooth Fano threefolds in the family <img mimesubtype=\"png\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319152445390-0178:S2050509424000057:S2050509424000057_inline3.png?pub-status=live\" type=\"\"> that satisfy one very explicit generality condition are K-stable.</img></img></img></p>","PeriodicalId":56000,"journal":{"name":"Forum of Mathematics Sigma","volume":"20 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"K-stable smooth Fano threefolds of Picard rank two\",\"authors\":\"Ivan Cheltsov, Elena Denisova, Kento Fujita\",\"doi\":\"10.1017/fms.2024.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove that all smooth Fano threefolds in the families <img mimesubtype=\\\"png\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319152445390-0178:S2050509424000057:S2050509424000057_inline1.png?pub-status=live\\\" type=\\\"\\\"> and <img mimesubtype=\\\"png\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319152445390-0178:S2050509424000057:S2050509424000057_inline2.png?pub-status=live\\\" type=\\\"\\\"> are K-stable, and we also prove that smooth Fano threefolds in the family <img mimesubtype=\\\"png\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240319152445390-0178:S2050509424000057:S2050509424000057_inline3.png?pub-status=live\\\" type=\\\"\\\"> that satisfy one very explicit generality condition are K-stable.</img></img></img></p>\",\"PeriodicalId\":56000,\"journal\":{\"name\":\"Forum of Mathematics Sigma\",\"volume\":\"20 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Forum of Mathematics Sigma\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/fms.2024.5\",\"RegionNum\":2,\"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":"Forum of Mathematics Sigma","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/fms.2024.5","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们证明了族中所有光滑的法诺三褶都是 K 稳定的，我们还证明了族中满足一个非常明确的一般性条件的光滑法诺三褶都是 K 稳定的。
K-stable smooth Fano threefolds of Picard rank two
We prove that all smooth Fano threefolds in the families and are K-stable, and we also prove that smooth Fano threefolds in the family that satisfy one very explicit generality condition are K-stable.
期刊介绍：
Forum of Mathematics, Sigma is the open access alternative to the leading specialist mathematics journals. Editorial decisions are made by dedicated clusters of editors concentrated in the following areas: foundations of mathematics, discrete mathematics, algebra, number theory, algebraic and complex geometry, differential geometry and geometric analysis, topology, analysis, probability, differential equations, computational mathematics, applied analysis, mathematical physics, and theoretical computer science. This classification exists to aid the peer review process. Contributions which do not neatly fit within these categories are still welcome.
Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas will be welcomed. All published papers will be free online to readers in perpetuity.
and 
are K-stable, and we also prove that smooth Fano threefolds in the family 
that satisfy one very explicit generality condition are K-stable.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
