Classification of Triples of Lattice Polytopes with a Given Mixed Volume

Authors

Gennadiy Averkov, BTU Cottbus-SenftenbergFollow
Christopher Borger, Otto-von-Guericke-Universität Magdeburg
Ivan Soprunov, Cleveland State UniversityFollow

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.

Comments

Open Access funding provided by Projekt DEAL.

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.