{"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":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"228 12","pages":"Article 107765"},"PeriodicalIF":0.8000,"publicationDate":"2024-12-01","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":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404924001622","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/7/2 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","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.
期刊介绍：
The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.
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