{"title":"Marked Godeaux surfaces with special bicanonical fibers","authors":"Frank-Olaf Schreyer , Isabel Stenger","doi":"10.1016/j.jpaa.2024.107765","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we study marked numerical Godeaux surfaces with special bicanonical fibers. Based on the construction method of marked Godeaux surfaces in <span>[12]</span> we give a complete characterization for the existence of hyperelliptic bicanonical fibers and torsion fibers. Moreover, we describe how the families of Reid and Miyaoka with torsion <span><math><mi>Z</mi><mo>/</mo><mn>3</mn><mi>Z</mi></math></span> and <span><math><mi>Z</mi><mo>/</mo><mn>5</mn><mi>Z</mi></math></span> arise in our homological setting.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022404924001622/pdfft?md5=24a063a7a56ffe64e021631c53abdb1f&pid=1-s2.0-S0022404924001622-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404924001622","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 this paper we study marked numerical Godeaux surfaces with special bicanonical fibers. Based on the construction method of marked Godeaux surfaces in [12] we give a complete characterization for the existence of hyperelliptic bicanonical fibers and torsion fibers. Moreover, we describe how the families of Reid and Miyaoka with torsion and arise in our homological setting.
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