On the topology of the moduli of tropical unramified p-covers

• Yassine El Maazouz ^[1] ; Paul Alexander Helminck ^[2] ; Felix Röhrle ^[3] ; Pedro Souza ^[4] ; Claudia He Yun ^[5]
  1. [1] California Institute of Technology

     California Institute of Technology

     Estados Unidos

     
  2. [2] Tohoku University

     Tohoku University

     Aoba-ku, Japón

     
  3. [3] University of Tübingen

     University of Tübingen

     Landkreis Tübingen, Alemania

     
  4. [4] Goethe University Frankfurt

     Goethe University Frankfurt

     Frankfurt, Alemania

     
  5. [5] University of Michigan–Ann Arbor

     University of Michigan–Ann Arbor

     City of Ann Arbor, Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 1, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-024-01007-4
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• Resumen

  • We study the topology of the moduli space of unramified Z/p-covers of tropical curves of genus g ≥ 2, where p is a prime number. We use recent techniques by Chan–Galatius–Payne to identify contractible subcomplexes of the moduli space. We then use this contractibility result to show that this moduli space is simply connected. In the case of genus 2, we determine the homotopy type of this moduli space for all primes p. This work is motivated by prospective applications to the top-weight cohomology of the space of prime cyclic étale covers of smooth algebraic curves.

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