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 $(\Gamma, D)$ consisting of a stable tropical curve $\Gamma$ and a divisor $D$ in the canonical linear system on $\Gamma$, we give a purely combinatorial condition to decide whether there is a smooth curve $X$ over a non-Archimedean field whose stable reduction has $\Gamma$ 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.

中文翻译：

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热带典型除数的可实现性

我们使用 Bainbridge-Chen-Gendron-Grushevsky-Moeller 最近关于阿贝尔微分地层紧化的结果，给出了等特征零中有效热带正则因数的可实现性问题的综合解决方案。给定一对 $(\Gamma, D)$ 由 $\Gamma$ 上的典型线性系统中的稳定热带曲线 $\Gamma$ 和除数 $D$ 组成，我们给出一个纯组合条件来决定是否存在非阿基米德场上的平滑曲线 $X$，其稳定归约以 $\Gamma$ 作为其对偶热带曲线以及专门针对 $D$ 的有效规范除数 $K_X$。在此过程中，我们开发了一个模理论框架来理解贝克的