JournalsjemsVol. 23, No. 1pp. 185–217

Realizability of tropical canonical divisors

  • Martin Möller

    Johann Wolfgang Goethe-Universität, Frankfurt, Germany
  • Martin Ulirsch

    Johann Wolfgang Goethe-Universität, Frankfurt, Germany
  • Annette Werner

    Johann Wolfgang Goethe-Universität, Frankfurt, Germany
Realizability of tropical canonical divisors cover
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Abstract

We use recent results by Bainbridge–Chen–Gendron–Grushevsky–Möller on compactifications of strata of abelian differentials to give a comprehensive solution to the realizability problem for effective tropical canonical divisors in equicharacteristic zero. Given a pair (Γ,D)(\Gamma, D) consisting of a stable tropical curve Γ\Gamma and a divisor DD in the canonical linear system on Γ\Gamma, we give a purely combinatorial condition to decide whether there is a smooth curve XX over a non-Archimedean field whose stable reduction has Γ\Gamma as its dual tropical curve together with an effective canonical divisor KXK_X that specializes to DD.

Cite this article

Martin Möller, Martin Ulirsch, Annette Werner, Realizability of tropical canonical divisors. J. Eur. Math. Soc. 23 (2021), no. 1, pp. 185–217

DOI 10.4171/JEMS/1009