{"title":"Holomorphic differential forms on moduli spaces of stable curves","authors":"Claudio Fontanari","doi":"10.1007/s10711-023-00851-6","DOIUrl":null,"url":null,"abstract":"Abstract We prove that the space of holomorphic p -forms on the moduli space $$\\overline{\\mathcal {M}}_{g,n}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mover> <mml:mi>M</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> </mml:math> of stable curves of genus g with n marked points vanishes for $$p=14, 16, 18$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>14</mml:mn> <mml:mo>,</mml:mo> <mml:mn>16</mml:mn> <mml:mo>,</mml:mo> <mml:mn>18</mml:mn> </mml:mrow> </mml:math> unconditionally and also for $$p=20$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>20</mml:mn> </mml:mrow> </mml:math> under a natural assumption in the case $$g=3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> . This result is consistent with the Langlands program and it is obtained by applying the Arbarello–Cornalba inductive approach to the cohomology of moduli spaces.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s10711-023-00851-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
Abstract We prove that the space of holomorphic p -forms on the moduli space $$\overline{\mathcal {M}}_{g,n}$$ M¯g,n of stable curves of genus g with n marked points vanishes for $$p=14, 16, 18$$ p=14,16,18 unconditionally and also for $$p=20$$ p=20 under a natural assumption in the case $$g=3$$ g=3 . This result is consistent with the Langlands program and it is obtained by applying the Arbarello–Cornalba inductive approach to the cohomology of moduli spaces.
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