Plucker Formulas for Plane Algebraic Curves with a Given Newton Polygon

Abstract

Let $C$ be a generic complex plane plane curve with a given Newton polygon $P$. We compute the number of its inflection points and bitangents (equivalently, the number of singularities of the projectively dual curve $C^{\vee }$). We also prove that $C^{\vee }$ has no singularities other than nodes and cusps for large enough polygons $P$.

30 pages, 5 figures