Divisors and curves on logarithmic mapping spaces

• Patrick Kennedy-Hunt ^[1] ; Navid Nabijou ^[2] ; Qaasim Shafi ^[3] ; Wanlong Zheng ^[1]
  1. [1] University of Cambridge

     University of Cambridge

     Cambridge District, Reino Unido

     
  2. [2] Queen Mary University of London

     Queen Mary University of London

     Reino Unido

     
  3. [3] University of Birmingham

     University of Birmingham

     Reino Unido

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 4, 2024, págs. 1-30
• Idioma: inglés
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• Resumen

  • We determine the rational class and Picard groups of the moduli space of stable logarithmic maps in genus zero, with target projective space relative a hyperplane.

    For the class group we exhibit an explicit basis consisting of boundary divisors. For the Picard group we exhibit a spanning set indexed by piecewise-linear functions on the tropicalisation. In both cases a complete set of boundary relations is obtained by pulling back the WDVV relations from the space of stable curves. Our proofs hinge on a controlled technique for manufacturing test curves in logarithmic mapping spaces, opening up the topology of these spaces to further study.