Complements of discriminants of real parabolic function singularities. II
Authors
V. A. Vassiliev
Abstract
We provide a complete list of the connected components of the spaces of non-discriminant functions within standard versal deformations of function singularities of classes $X_9$, $J_{10}$ and $P_8^1$ (as well as a partial list for the remaining class, $P_8^2$). Thus, we prove (and improve in one particular case) the corresponding conjectures from the previous work \cite{para} with the same title. As an application, we enumerate all local Petrovskii lacunas near arbitrary parabolic singularities of wavefronts of hyperbolic PDEs. In particular, we discover a new local lacuna at the $P_8^2$ singularities. We also show that the complements of the discriminant varieties of $X_9^+$ and $P_8^1$ singularities have nontrivial one-dimensional homology groups, unlike all simple singularities.
