{"title":"带对数正则奇点的膨胀","authors":"G. Sankaran, F. Santos","doi":"10.2140/gt.2021.25.2145","DOIUrl":null,"url":null,"abstract":"We show that the minimum weight of a weighted blow-up of $\\mathbf A^d$ with $\\varepsilon$-log canonical singularities is bounded by a constant depending only on $\\varepsilon $ and $d$. This was conjectured by Birkar. \nUsing the recent classification of $4$-dimensional empty simplices by Iglesias-Vali\\~no and Santos, we work out an explicit bound for blowups of $\\mathbf A^4$ with terminal singularities: the smallest weight is always at most $32$, and at most $6$ in all but finitely many cases.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Blowups with log canonical singularities\",\"authors\":\"G. Sankaran, F. Santos\",\"doi\":\"10.2140/gt.2021.25.2145\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the minimum weight of a weighted blow-up of $\\\\mathbf A^d$ with $\\\\varepsilon$-log canonical singularities is bounded by a constant depending only on $\\\\varepsilon $ and $d$. This was conjectured by Birkar. \\nUsing the recent classification of $4$-dimensional empty simplices by Iglesias-Vali\\\\~no and Santos, we work out an explicit bound for blowups of $\\\\mathbf A^4$ with terminal singularities: the smallest weight is always at most $32$, and at most $6$ in all but finitely many cases.\",\"PeriodicalId\":55105,\"journal\":{\"name\":\"Geometry & Topology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2019-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometry & Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/gt.2021.25.2145\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometry & Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/gt.2021.25.2145","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
我们证明了$\mathbf a ^d$与$\varepsilon$-log正则奇点的加权爆破的最小权值由一个仅依赖于$\varepsilon$和$d$的常数所限定。这是比尔卡的推测。利用Iglesias-Vali\~no和Santos最近对$ $4维空简式的分类，我们得到了$ $ mathbf A^4$具有端点奇点的膨胀的显式界:最小的权重总是最多$32$，除了有限多的情况外，在所有情况下最多$6$。
We show that the minimum weight of a weighted blow-up of $\mathbf A^d$ with $\varepsilon$-log canonical singularities is bounded by a constant depending only on $\varepsilon $ and $d$. This was conjectured by Birkar.
Using the recent classification of $4$-dimensional empty simplices by Iglesias-Vali\~no and Santos, we work out an explicit bound for blowups of $\mathbf A^4$ with terminal singularities: the smallest weight is always at most $32$, and at most $6$ in all but finitely many cases.
期刊介绍：
Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers.
The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.
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