Obstructions to Approximating Tropical Curves in Surfaces Via Intersection Theory
Erwan Brugallé, Kristin Shaw · Canadian Journal of Mathematics · 2014
Abstract We provide some new local obstructions to approximating tropical curves in smooth tropical surfaces. These obstructions are based on a relation between tropical and complex intersection theories, which is also established here. We give two applications of the methods developed in this paper. First we classify all locally irreducible approximable 3–valent fan tropical curves in a fan tropical plane. Secondly, we prove that a generic non–singular tropical surface in tropical projective 3–space contains finitely many approximable tropical lines if it is of degree 3, and contains no approximable tropical lines if it is of degree 4 or more.