A generalization of simple Harnack curves
Lionel Lang · arXiv (Cornell University) · 2015
Simple Harnack curves, introduced in [Mik00], are smooth real algebraic curves in maximal position in toric surfaces. In the present paper, we suggest a natural generalization of simple Harnack curves by relaxing the smoothness assumption. After mentioning some of their properties, we address the question of their construction. We dene tropical Harnack curves and show that their approximation using Mikhalkin’s machinery produces many new example of simple Harnack curves. We determine the topological classication of simple Harnack curves with a hyperbolic node in the fashion of [Mik00], and show that the space of such curves can be locally parametrized by the space of their tropical avatars, in the spirit of [KO06].