Realizability of tropical canonical divisors Moeller, Martin Ulirsch, Martin Werner, Annette We use recent results by Bainbridge-Chen-Gendron-Grushevsky-Moeller 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 $(Γ, D)$ consisting of a stable tropical curve $Γ$ and a divisor $D$ in the canonical linear system on $Γ$, we give a purely combinatorial condition to decide whether there is a smooth curve $X$ over a non-Archimedean field whose stable reduction has $Γ$ as its dual tropical curve together with a effective canonical divisor $K_X$ that specializes to $D$. Along the way, we develop a moduli-theoretic framework to understand Baker's specialization of divisors from algebraic to tropical curves as a natural toroidal tropicalization map in the sense of Abramovich-Caporaso-Payne. 2017 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_6501 https://ris.uni-paderborn.de/record/66333 Moeller M, Ulirsch M, Werner A. Realizability of tropical canonical divisors. <i>arXiv:171006401</i>. Published online 2017. doi:<a href="https://doi.org/10.4171/JEMS/1009">10.4171/JEMS/1009</a> eng info:eu-repo/semantics/altIdentifier/doi/10.4171/JEMS/1009 info:eu-repo/semantics/altIdentifier/arxiv/1710.06401 info:eu-repo/semantics/closedAccess