article Martin Moeller author Martin Ulirsch author 114697 Annette Werner author 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 eng 1710.0640110.4171/JEMS/1009 Moeller, Martin, et al. “Realizability of Tropical Canonical Divisors.” <i>ArXiv:1710.06401</i>, 2017, doi:<a href="https://doi.org/10.4171/JEMS/1009">10.4171/JEMS/1009</a>. 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> @article{Moeller_Ulirsch_Werner_2017, title={Realizability of tropical canonical divisors}, DOI={<a href="https://doi.org/10.4171/JEMS/1009">10.4171/JEMS/1009</a>}, journal={arXiv:1710.06401}, author={Moeller, Martin and Ulirsch, Martin and Werner, Annette}, year={2017} } Moeller, M., Ulirsch, M., &#38; Werner, A. (2017). Realizability of tropical canonical divisors. <i>ArXiv:1710.06401</i>. <a href="https://doi.org/10.4171/JEMS/1009">https://doi.org/10.4171/JEMS/1009</a> M. Moeller, M. Ulirsch, and A. Werner, “Realizability of tropical canonical divisors,” <i>arXiv:1710.06401</i>, 2017, doi: <a href="https://doi.org/10.4171/JEMS/1009">10.4171/JEMS/1009</a>. M. Moeller, M. Ulirsch, A. Werner, ArXiv:1710.06401 (2017). Moeller, Martin, Martin Ulirsch, and Annette Werner. “Realizability of Tropical Canonical Divisors.” <i>ArXiv:1710.06401</i>, 2017. <a href="https://doi.org/10.4171/JEMS/1009">https://doi.org/10.4171/JEMS/1009</a>. 663332026-07-08T07:06:32Z2026-07-08T09:40:36Z