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arXiv · 1902.00891

Classification of triples of lattice polytopes with a given mixed volume

Gennadiy Averkov·Christopher Borger·Ivan Soprunov
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Abstract

We present an algorithm for the classification of triples of lattice polytopes with a given mixed volume $m$ in 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.

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Gennadiy Averkov, Christopher Borger, Ivan Soprunov. 2020-10-21. Classification of triples of lattice polytopes with a given mixed volume. https://doi.org/10.1007/s00454-020-00246-4

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