{"title":"On Weak bounded negativity conjecture","authors":"Snehajit Misra, Nabanita Ray","doi":"arxiv-2408.15187","DOIUrl":null,"url":null,"abstract":"In the first part of this article, we give bounds on self-intersections $C^2$\nof integral curves $C$ on blow-ups $Bl_nX$ of surfaces $X$ with the\nanti-cannonical divisor $-K_X$ effective. In the last part, we prove the weak\nbounded negativity for self-intersections $C^2$ of integral curves $C$ in a\nfamily of surfaces $f:Y\\longrightarrow B$ where $B$ is a smooth curve.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.15187","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In the first part of this article, we give bounds on self-intersections $C^2$
of integral curves $C$ on blow-ups $Bl_nX$ of surfaces $X$ with the
anti-cannonical divisor $-K_X$ effective. In the last part, we prove the weak
bounded negativity for self-intersections $C^2$ of integral curves $C$ in a
family of surfaces $f:Y\longrightarrow B$ where $B$ is a smooth curve.
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