Tropical limit of log-inflection points for planar curves

Abstract

The paper describes behavior of log-inflection points of curves in $({\mathbb{C}}^{\ast }{)}^2$ under passing to the tropical limit. We show that such points accumulate by pairs at the midpoints of bounded edges in the limiting tropical curve. Log-inflection points are points of inflection with respect to the parallelization of $({\mathbb{C}}^{\ast }{)}^2$ given by the multiplicative group law.

arXiv comment14 pages, 10 figures