Document Type
Article
Publication Date
10-2020
Publication Title
Discrete & Computational Geometry
Abstract
We present an algorithm for the classification of triples of lattice polytopes with a given mixed volumemin dimension 3. It is known that the classification can be reduced to the enumeration of so-called irreducible triples, the number of which is finite for fixed m. Following this algorithm, we enumerate all irreducible triples of normalized mixed volume up to 4 that are inclusion-maximal. This produces a classification of generic trivariate sparse polynomial systems with up to 4 solutions in the complex torus, up to monomial changes of variables. By a recent result of Esterov, this leads to a description of all generic trivariate sparse polynomial systems that are solvable by radicals.
Repository Citation
Averkov, Gennadiy; Borger, Christopher; and Soprunov, Ivan, "Classification of Triples of Lattice Polytopes with a Given Mixed Volume" (2020). Mathematics and Statistics Faculty Publications. 338.
https://engagedscholarship.csuohio.edu/scimath_facpub/338
DOI
10.1007/s00454-020-00246-4
Version
Publisher's PDF
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Comments
Open Access funding provided by Projekt DEAL.