2024/09/26 by Sukenaga, Masayuki
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2409.18348
When a tropical rational function φon Rn is given, we can represent it as φ=f-g with tropical polynomials f and g. We develop the duality theorem for tropical rational functions to define the volume of the pair (f, g). We show that when n=1, we can find a representation of φ(x) ≠ -∞ as f(x)-g(x) with the pair (f, g) of minimum volume. The dual subdivision of f(x) ⊕ (yg(x)) is unique up to translation, but when n=2 this is not true.