M. Dumnicki, L. Farnik, Krishna Hanumanthu, G. Malara, T. Szemberg, J. Szpond, H. Tutaj-Gasinska
{"title":"Negative curves on special rational surfaces","authors":"M. Dumnicki, L. Farnik, Krishna Hanumanthu, G. Malara, T. Szemberg, J. Szpond, H. Tutaj-Gasinska","doi":"10.18778/8142-814-9.06","DOIUrl":null,"url":null,"abstract":"We study negative curves on surfaces obtained by blowing up special configurations of points in the complex projective palne. Our main results concern the following configurations: very general points on a cubic, 3-torsion points on an elliptic curve and nine Fermat points. As a consequence of our analysis, we also show that the Bounded Negativity Conjecture holds for the surfaces we consider. The note contains also some problems for future attention.","PeriodicalId":273656,"journal":{"name":"Analytic and Algebraic Geometry 3","volume":"45 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analytic and Algebraic Geometry 3","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18778/8142-814-9.06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We study negative curves on surfaces obtained by blowing up special configurations of points in the complex projective palne. Our main results concern the following configurations: very general points on a cubic, 3-torsion points on an elliptic curve and nine Fermat points. As a consequence of our analysis, we also show that the Bounded Negativity Conjecture holds for the surfaces we consider. The note contains also some problems for future attention.
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