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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
  • DOI: 10.1007/s00029-024-00956-0
  • Enlaces
  • 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.

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