Modality of a singularity

Summary

The modality of a critical point of a function counts continuous parameters, called moduli. It is the number of moduli needed to describe all nearby critical points up to a change of coordinates. Germs of modality $0$ are the simple singularities: only finitely many types occur near them. Arnold introduced the notion and classified the germs of modality $0$, $1$ and $2$. Modality measures how far the classification of singularities is from being a finite list.