2024/01/11 by Ivan Soprunov, Soprunov, Ivan, Jenya Soprunova +1
Computer Science · Mathematics · #Polynomial and algebraic computation #Algebraic Geometry and Number Theory #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2401.06111
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.