{"title":"The (almost) integral Chow ring of ℳ̅3","authors":"Michele Pernice","doi":"10.1515/crelle-2024-0034","DOIUrl":null,"url":null,"abstract":"\n <jats:p>This paper is the fourth in a series of four papers aiming to describe the (almost integral) Chow ring of <jats:inline-formula>\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:msub>\n <m:mover accent=\"true\">\n <m:mi mathvariant=\"script\">M</m:mi>\n <m:mo>̄</m:mo>\n </m:mover>\n <m:mn>3</m:mn>\n </m:msub>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_crelle-2024-0034_ineq_0001.png\"/>\n <jats:tex-math>\\overline{\\mathcal{M}}_{3}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula>, the moduli stack of stable curves of genus 3.\nIn this paper, we finally compute the Chow ring of <jats:inline-formula>\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:msub>\n <m:mover accent=\"true\">\n <m:mi mathvariant=\"script\">M</m:mi>\n <m:mo>̄</m:mo>\n </m:mover>\n <m:mn>3</m:mn>\n </m:msub>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_crelle-2024-0034_ineq_0001.png\"/>\n <jats:tex-math>\\overline{\\mathcal{M}}_{3}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula> with <jats:inline-formula>\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mrow>\n <m:mi mathvariant=\"double-struck\">Z</m:mi>\n <m:mo></m:mo>\n <m:mrow>\n <m:mo stretchy=\"false\">[</m:mo>\n <m:mrow>\n <m:mn>1</m:mn>\n <m:mo>/</m:mo>\n <m:mn>6</m:mn>\n </m:mrow>\n <m:mo stretchy=\"false\">]</m:mo>\n </m:mrow>\n </m:mrow>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_crelle-2024-0034_ineq_0003.png\"/>\n <jats:tex-math>\\mathbb{Z}[1/6]</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula>-coefficients.</jats:p>","PeriodicalId":508691,"journal":{"name":"Journal für die reine und angewandte Mathematik (Crelles Journal)","volume":"91 10","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal für die reine und angewandte Mathematik (Crelles Journal)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/crelle-2024-0034","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
This paper is the fourth in a series of four papers aiming to describe the (almost integral) Chow ring of M̄3\overline{\mathcal{M}}_{3}, the moduli stack of stable curves of genus 3.
In this paper, we finally compute the Chow ring of M̄3\overline{\mathcal{M}}_{3} with Z[1/6]\mathbb{Z}[1/6]-coefficients.
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