Superabundant curves and the Artin fan
arXiv:1504.08199
Abstract
We prove that every balanced 1-dimensional polyhedral complex arises as the tropicalization of a smooth curve over a non-Archimedean field mapping to a toric Artin fan, namely the quotient of a toric variety by its dense torus.
arXiv comment9 pages, 1 figure. v2: Restructured proof of Main Theorem. Other minor changes. To appear in Int. Math. Res. Not