in some codimension $1$ cases, locally by Suwa (see *loc. cit.*) and on ${\mathbb{P}}^n$ by Molinuevo in [@moli].

Recently we have related the study of unfoldings and singularities of a codimension $1$ foliation on ${\mathbb{P}}^n$. Indeed, in [@mmq] we define a homogeneous ideal $I(\omega)$ defining a subscheme of the singular scheme of $\omega$ (see below for precise definitions), the elements of degree equal to the degree of $\omega$ in $I(\omega)$ are in natural correspondence with the infinitesimal unfoldings of $\omega$. Under generic conditions we can prove that if $K(\omega)$ is the ideal defining the closure of the variety of Kupka points then $\sqrt{I(\omega)}=\sqrt{K(\omega)}$, using this result we were able to compute the unfoldings of foliations of codimension $1$ on ${\mathbb{P}}^n$ with split tangent sheaf and also prove the existence of Kupka points for every foliation in ${\mathbb{P}}^n$ with reduced singular scheme.

Main results {#main-results .unnumbered}
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Our aim in this article is to generalize previous results on the relation of unfoldings and singular points of a foliation to arbitrary codimension and to foliations on a non-singular projective variety. We also begin a study of this relation in toric varieties by making use of the Cox ring of the variety and 