Geometry of bifurcation sets of generic unfoldings of corank two functions

Abstract

We study the geometry of bifurcation sets of generic unfoldings of $D_4^\pm$-functions. Taking blow-ups, we show each of the bifurcation sets of $D_4^\pm$-functions admit a parametrization as a surface in $R^3$. Using this parametrization, we investigate the behavior of the Gaussian curvature and the principal curvatures. Furthermore, we investigate the number of ridge curves and subparabolic curves near their singular point.