Non-degeneracy of the discriminant
  Let $(l,f):(C^2,0)\rightarrow (C^2,0)$ be the germ of a holomorphic mapping such that $l=0$ is a smooth curve which is not a branch of the singular curve $f=0$. The direct image of the critical locus of this mapping is called the discriminant curve. In this paper we study the pairs $(l,f)$ for which the discriminant curve is non-degenerate in the Kouchnirenko sense. 
Evelia R. Garc\'ia Barroso, Janusz Gwozdziewicz and Andrzej Lenarcik
math.AG