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arXiv · 2401.06111

The volume polynomial of lattice polygons

Ivan Soprunov·Jenya Soprunova
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Abstract

We prove that every indefinite quadratic form with non-negative integer coefficients is the volume polynomial of a pair of lattice polygons. This solves the discrete version of the Heine-Shephard problem for two bodies in the plane. As an application, we show how to construct a pair of planar tropical curves (or a pair of divisors on a toric surface) with given intersection number and self-intersection numbers.

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Ivan Soprunov, Jenya Soprunova. 2024-01-11. The volume polynomial of lattice polygons. https://arxiv.org/abs/2401.06111

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