@article{66350,
  abstract     = {{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.}},
  author       = {{Cheung, Man-Wai and Fantini, Lorenzo and Park, Jennifer and Ulirsch, Martin}},
  journal      = {{arXiv:1410.4152}},
  title        = {{{Faithful realizability of tropical curves}}},
  year         = {{2014}},
}