  The hypertoric variety $\mathfrak{M}_{\mathcal{A}}$ defined by an affine
arrangement $\mathcal{A}$ admits a natural tropicalization, induced by its
embedding in a Lawrence toric variety. We explicitly describe the polyhedral
structure of this tropicalization. Using a recent result of Gubler, Rabinoff,
and Werner, we prove that there is a continuous section of the tropicalization
map.

Algebraic Geometry;Combinatorics