Tropical curves of unibranch points and hypertangency
Abstract
We study plane curves meeting at a single unibranch point and show that they must satisfy two equivalent conditions. A geometric one: the tropical curves associated to the contact point are isomorphic. An arithmetic one: the local invariants at the contact point satisfy a simple relation. Furthermore, we prove closed formulas for the delta-invariant of a unibranch singularity, and for the dimension of the locus of curves with an assigned unibranch point. Our work is motivated by interest in the Lang's exceptional set.
Fields of Study & Subjects
Meromorphic and Entire Functions
Polynomial and algebraic computation
Publication details
- Journal / source
- Pure and Applied Mathematics Quarterly
- Publisher
- International Press of Boston
- Volume
- 22
- Issue
- 2
- Pages
- 477–505
- Publication date
- 1 January 2026
- Language
- EN