Faithful realizability of tropical curves Cheung, Man-Wai Fantini, Lorenzo Park, Jennifer Ulirsch, Martin 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. 2014 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_6501 https://ris.uni-paderborn.de/record/66350 Cheung M-W, Fantini L, Park J, Ulirsch M. Faithful realizability of tropical curves. <i>arXiv:14104152</i>. Published online 2014. eng info:eu-repo/semantics/altIdentifier/arxiv/1410.4152 info:eu-repo/semantics/closedAccess