Papers › The volume polynomial of lattice polygons
The volume polynomial of lattice polygons
Ivan Soprunov, Jenya Soprunova
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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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