The number of vertices of a tropical curve is bounded by its area

  • Tony Yue Yu

    Université Paris-Diderot Paris 7, France

Abstract

We introduce the notion of tropical area of a tropical curve defined in an open subset of . We prove that the number of vertices of a tropical curve is bounded by the area of the curve. The approach is totally elementary yet tricky. Our proof employs ideas from intersection theory in algebraic geometry. The result can be interpreted as the fact that the moduli space of tropical curves with bounded area is of finite type.

Cite this article

Tony Yue Yu, The number of vertices of a tropical curve is bounded by its area. Enseign. Math. 60 (2014), no. 3/4, pp. 257–271

DOI 10.4171/LEM/60-3/4-3