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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 consisting of a stable tropical curve and a divisor in the canonical linear system on , we give a purely combinatorial condition to decide whether there is a smooth curve over a non-Archimedean field whose stable reduction has as its dual tropical curve together with an effective canonical divisor that specializes to .
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Martin Möller, Martin Ulirsch, Annette Werner, Realizability of tropical canonical divisors. J. Eur. Math. Soc. 23 (2021), no. 1, pp. 185–217DOI 10.4171/JEMS/1009