Geometry of planar log-fronts

Abstract

The log-front of two plane curves P(z,w)=0 and Q(z,w)=0 is the locus of (a,b) such that Q(az,bw)=0 is tangent to P(z,w)=0. Log-fronts generalize dual curves, wave fronts, and arise naturally in the theory of random surfaces. Our goal in this paper is to prove analogs of Plucker and Klein formulas for log-fronts.

Dedicated to Askold Khovanskii on the occasion of his 60th birthday