Faithful realizability of tropical curves

@article{Cheung2014FaithfulRO,
  title={Faithful realizability of tropical curves},
  author={Man-Wai Cheung and Lorenzo Fantini and Jennifer Park and Martin Ulirsch},
  journal={arXiv: Algebraic Geometry},
  year={2014}
}
We study whether a given tropical curve $\Gamma$ in $\mathbb{R}^n$ can be realized as the tropicalization of an algebraic curve whose non-archimedean skeleton is faithfully represented by $\Gamma$. 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… 

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