{"abstract":[{"lang":"eng","text":"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."}],"citation":{"short":"M. Ulirsch, D. Zakharov, ArXiv:1910.01499 (2019).","chicago":"Ulirsch, Martin, and Dmitry Zakharov. “Tropical Double Ramification Loci.” <i>ArXiv:1910.01499</i>, 2019.","ieee":"M. Ulirsch and D. Zakharov, “Tropical double ramification loci,” <i>arXiv:1910.01499</i>. 2019.","apa":"Ulirsch, M., &#38; Zakharov, D. (2019). Tropical double ramification loci. In <i>arXiv:1910.01499</i>.","bibtex":"@article{Ulirsch_Zakharov_2019, title={Tropical double ramification loci}, journal={arXiv:1910.01499}, author={Ulirsch, Martin and Zakharov, Dmitry}, year={2019} }","ama":"Ulirsch M, Zakharov D. Tropical double ramification loci. <i>arXiv:191001499</i>. Published online 2019.","mla":"Ulirsch, Martin, and Dmitry Zakharov. “Tropical Double Ramification Loci.” <i>ArXiv:1910.01499</i>, 2019."},"publication":"arXiv:1910.01499","type":"preprint","date_created":"2026-07-08T06:49:12Z","external_id":{"arxiv":["1910.01499"]},"date_updated":"2026-07-08T06:49:19Z","author":[{"last_name":"Ulirsch","first_name":"Martin","full_name":"Ulirsch, Martin","id":"114697"},{"full_name":"Zakharov, Dmitry","first_name":"Dmitry","last_name":"Zakharov"}],"status":"public","title":"Tropical double ramification loci","year":"2019","user_id":"82981","_id":"66322","language":[{"iso":"eng"}]}