Faithful tropicalization of hypertoric varieties
Max B. Kutler

TL;DR
This paper explicitly describes the polyhedral structure of the tropicalization of hypertoric varieties and proves the existence of a continuous section of the tropicalization map, advancing understanding of their tropical geometry.
Contribution
It provides an explicit description of the tropicalization's polyhedral structure and establishes a continuous section of the tropicalization map for hypertoric varieties.
Findings
Explicit polyhedral description of hypertoric variety tropicalization
Existence of a continuous section of the tropicalization map
Advancement in tropical geometry of hypertoric varieties
Abstract
The hypertoric variety defined by an affine arrangement 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.
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Advanced Combinatorial Mathematics
