integrable $1$-form $\omega$ is a point $p$ such that $\omega(p)=0$ and $d\omega(p)\neq 0$. Kupka showed that this type of singularity of codimension $1$ foliation is stable, meaning that if $\omega_t$ is a family of integrable $1$-forms parameterized by $t$ and $\omega_0$ has a Kupka singularity then $\omega_t$ also has a Kupka singularity for small enough $t$. Also if a foliation have a Kupka singularity then there is a codimension $2$ subvariety whose points are singular points of the foliation. Kupka singularities were generalized to arbitrary codimension by de Medeiros in [@deMedTesis], where stability for this singularities is proved in general. In codimension $q$ Kupka singularities come in subvarieties of codimension less or equal than $q+1$. In codimension $1$ there are many results relating the geometry of the variety of Kupka points with the global properties of the foliation, see *e.g.*: [@omegar-ivan; @omegar-kupka]. In higher codimension there is the work of Calvo-Andrade [@omegar2009].

A third subject we look upon in this work is the study of the unfoldings of a foliation. Unfoldings in the context of foliations were introduced independently by Suwa and Mattei in different contexts, see [@suwa-review] for a survey on the subject. Unfoldings of foliations where computed mostly 