{"title":"Sarkisov links with centre space curves on smooth cubic surfaces","authors":"Sokratis Zikas","doi":"10.5565/publmat6722301","DOIUrl":null,"url":null,"abstract":"We construct and study Sarkisov links obtained by blowing up smooth space curves lying on smooth cubic surfaces. We restrict our attention to the case where the blowup is not weak Fano. Together with the results of arXiv:1106.3716 which cover the weak Fano case, we provide a classification of all such curves. This is achieved by computing all curves which satisfy certain necessary criteria on their multisecant curves and then constructing the Sarkisov link step by step.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2020-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Publicacions Matematiques","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5565/publmat6722301","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
We construct and study Sarkisov links obtained by blowing up smooth space curves lying on smooth cubic surfaces. We restrict our attention to the case where the blowup is not weak Fano. Together with the results of arXiv:1106.3716 which cover the weak Fano case, we provide a classification of all such curves. This is achieved by computing all curves which satisfy certain necessary criteria on their multisecant curves and then constructing the Sarkisov link step by step.
期刊介绍：
Publicacions Matemàtiques is a research mathematical journal published by the Department of Mathematics of the Universitat Autònoma de Barcelona since 1976 (before 1988 named Publicacions de la Secció de Matemàtiques, ISSN: 0210-2978 print, 2014-4369 online). Two issues, constituting a single volume, are published each year. The journal has a large circulation being received by more than two hundred libraries all over the world. It is indexed by Mathematical Reviews, Zentralblatt Math., Science Citation Index, SciSearch®, ISI Alerting Services, COMPUMATH Citation Index®, and it participates in the Euclid Project and JSTOR. Free access is provided to all published papers through the web page.
Publicacions Matemàtiques is a non-profit university journal which gives special attention to the authors during the whole editorial process. In 2019, the average time between the reception of a paper and its publication was twenty-two months, and the average time between the acceptance of a paper and its publication was fifteen months. The journal keeps on receiving a large number of submissions, so the authors should be warned that currently only articles with excellent reports can be accepted.
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