{"title":"关于弱有界否定性猜想","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":"{\"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}","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}
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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