Planar tropical caustics: trivalency and convexity
Algebraic Geometry
2025-10-03 v2 Combinatorics
Metric Geometry
Number Theory
Symplectic Geometry
Abstract
Tropical caustic of a convex domain on the plane is a canonically associated tropical analytic curve inside the domain. In this note we give a graphical proof for the classification of its intermediate vertices, implying in particular that they are always trivalent. Apart from that we explain how various known examples of tropical caustics are constructed and discuss the possibility of relaxing the convexity condition for the domain.
Keywords
Cite
@article{arxiv.2503.11137,
title = {Planar tropical caustics: trivalency and convexity},
author = {Mikhail Shkolnikov},
journal= {arXiv preprint arXiv:2503.11137},
year = {2025}
}
Comments
Accepted to Serdica Mathematical Journal 2025