Holomorphic forms and non-tautological cycles on moduli spaces of curves

• Veronica Arena ^[1] ; Samir Canning ^[2] ; Emily Clader ^[3] ; Richard Haburcak ^[4] ; Amy Q. Li ^[5] ; Siao Chi Mok ^[1] ; Carolina Tamborini ^[6]
  1. [1] University of Cambridge

     University of Cambridge

     Cambridge District, Reino Unido

     
  2. [2] Swiss Federal Institute of Technology in Zurich

     Swiss Federal Institute of Technology in Zurich

     Zürich, Suiza

     
  3. [3] San Francisco State University

     San Francisco State University

     Estados Unidos

     
  4. [4] Ohio State University

     Ohio State University

     City of Columbus, Estados Unidos

     
  5. [5] University of Texas at Austin

     University of Texas at Austin

     Estados Unidos

     
  6. [6] Universität Duisburg Essen, Essen, Germany

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 3, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01038-5
• Enlaces
  • Texto completo
• Resumen

  • We prove, for infinitely many values of g and n, the existence of non-tautological algebraic cohomology classes on the moduli space Mg,n of smooth, genus-g, npointed curves. In particular, when n = 0, our results show that there exist nontautological algebraic cohomology classes on Mg for g = 12 and all g ≥ 16. These results generalize the work of Graber–Pandharipande and van Zelm, who proved that the classes of particular loci of bielliptic curves are non-tautological and thereby exhibited the only previously-known non-tautological class on any Mg: the bielliptic cycle on M12. We extend their work by using the existence of holomorphic forms on certain moduli spaces Mg,n to produce non-tautological classes with nontrivial restriction to the interior, via which we conclude that the classes of many new doublecover loci are non-tautological.

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