[{"user_id":"82981","language":[{"iso":"eng"}],"_id":"66350","date_updated":"2026-07-08T07:23:19Z","author":[{"first_name":"Man-Wai","last_name":"Cheung","full_name":"Cheung, Man-Wai"},{"full_name":"Fantini, Lorenzo","first_name":"Lorenzo","last_name":"Fantini"},{"full_name":"Park, Jennifer","last_name":"Park","first_name":"Jennifer"},{"full_name":"Ulirsch, Martin","last_name":"Ulirsch","first_name":"Martin"}],"status":"public","title":"Faithful realizability of tropical curves","year":"2014","type":"journal_article","date_created":"2026-07-08T07:22:48Z","external_id":{"arxiv":["1410.4152"]},"abstract":[{"text":"We study whether a given tropical curve $Γ$ in $\\mathbb{R}^n$ can be realized as the tropicalization of an algebraic curve whose non-archimedean skeleton is faithfully represented by $Γ$. We give an affirmative answer to this question for a large class of tropical curves that includes all trivalent tropical curves, but also many tropical curves of higher valence. We then deduce that for every metric graph $G$ with rational edge lengths there exists a smooth algebraic curve in a toric variety whose analytification has skeleton $G$, and the corresponding tropicalization is faithful. Our approach is based on a combination of the theory of toric schemes over discrete valuation rings and logarithmically smooth deformation theory, expanding on a framework introduced by Nishinou and Siebert.","lang":"eng"}],"citation":{"ieee":"M.-W. Cheung, L. Fantini, J. Park, and M. Ulirsch, “Faithful realizability of tropical curves,” <i>arXiv:1410.4152</i>, 2014.","apa":"Cheung, M.-W., Fantini, L., Park, J., &#38; Ulirsch, M. (2014). Faithful realizability of tropical curves. <i>ArXiv:1410.4152</i>.","chicago":"Cheung, Man-Wai, Lorenzo Fantini, Jennifer Park, and Martin Ulirsch. “Faithful Realizability of Tropical Curves.” <i>ArXiv:1410.4152</i>, 2014.","short":"M.-W. Cheung, L. Fantini, J. Park, M. Ulirsch, ArXiv:1410.4152 (2014).","mla":"Cheung, Man-Wai, et al. “Faithful Realizability of Tropical Curves.” <i>ArXiv:1410.4152</i>, 2014.","bibtex":"@article{Cheung_Fantini_Park_Ulirsch_2014, title={Faithful realizability of tropical curves}, journal={arXiv:1410.4152}, author={Cheung, Man-Wai and Fantini, Lorenzo and Park, Jennifer and Ulirsch, Martin}, year={2014} }","ama":"Cheung M-W, Fantini L, Park J, Ulirsch M. Faithful realizability of tropical curves. <i>arXiv:14104152</i>. Published online 2014."},"publication":"arXiv:1410.4152"}]