Article
Classification of Triples of Lattice Polytopes with a Given Mixed Volume
Discrete & Computational Geometry
Document Type
Article
Publication Date
10-1-2020
Disciplines
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.
DOI
10.1007/s00454-020-00246-4
Version
Publisher's PDF
Creative Commons License
Creative Commons Attribution 4.0 International
Citation Information
Gennadiy Averkov, Christopher Borger and Ivan Soprunov. "Classification of Triples of Lattice Polytopes with a Given Mixed Volume" Discrete & Computational Geometry (2020) Available at: http://works.bepress.com/ivan-soprunov/20/
Open Access funding provided by Projekt DEAL.