preprint Martin Ulirsch author 114697 Dmitry Zakharov author Motivated by the realizability problem for principal tropical divisors with a fixed ramification profile, we explore the tropical geometry of the double ramification locus in $\mathcal{M}_{g,n}$.There are two ways to define a tropical analogue of the double ramification locus: one as a locus of principal divisors, the other as a locus of finite effective ramified covers of a tree. We show that both loci admit a structure of a generalized cone complex in $M_{g,n}^{trop}$, with the latter contained in the former. We prove that the locus of principal divisors has cones of codimension zero in $M_{g,n}^{trop}$, while the locus of ramified covers has the expected codimension $g$. This solves the deformation-theoretic part of the realizability problem for principal divisors, reducing it to the so-called Hurwitz existence problem for covers of a fixed ramification type. 2019 eng 1910.01499 Ulirsch, Martin, and Dmitry Zakharov. “Tropical Double Ramification Loci.” <i>ArXiv:1910.01499</i>, 2019. @article{Ulirsch_Zakharov_2019, title={Tropical double ramification loci}, journal={arXiv:1910.01499}, author={Ulirsch, Martin and Zakharov, Dmitry}, year={2019} } Ulirsch M, Zakharov D. Tropical double ramification loci. <i>arXiv:191001499</i>. Published online 2019. M. Ulirsch and D. Zakharov, “Tropical double ramification loci,” <i>arXiv:1910.01499</i>. 2019. Ulirsch, M., &#38; Zakharov, D. (2019). Tropical double ramification loci. In <i>arXiv:1910.01499</i>. Ulirsch, Martin, and Dmitry Zakharov. “Tropical Double Ramification Loci.” <i>ArXiv:1910.01499</i>, 2019. M. Ulirsch, D. Zakharov, ArXiv:1910.01499 (2019). 663222026-07-08T06:49:12Z2026-07-08T06:49:19Z