Balancing properties of tropical moduli maps
Algebraic Geometry
2026-02-10 v2
Abstract
Given a family of parameterized algebraic curves over a strictly semistable pair, we show that the simultaneous tropicalization of the curves in the family forms a family of parameterized tropical curves over the skeleton of the strictly semistable pair. We show that the induced tropical moduli map satisfies a certain balancing condition, which allows us to describe properties of its image and deduce a new liftability criterion.
Keywords
Cite
@article{arxiv.2403.15686,
title = {Balancing properties of tropical moduli maps},
author = {Karl Christ and Xiang He and Ilya Tyomkin},
journal= {arXiv preprint arXiv:2403.15686},
year = {2026}
}
Comments
Final version, accepted to Bulletin of the London Mathematical Society