Rational pullbacks of toric foliations

Abstract This article is dedicated to the study of singular codimension-one foliations ℱ {\mathcal{F}} on a simplicial complete toric variety X and their pullbacks by dominant rational maps φ : ℙ n ⇢ X {\varphi:\mathbb{P}^{n}\dashrightarrow X} . First, we describe singularities * ⁢ {\varphi^{*}\mathcal{F}} for generic pair ( , stretchy="false">) {(\varphi,\mathcal{F})} Then show that first-order deformations arising from unfoldings are families form ε {\varphi_{\varepsilon}^{*}\mathcal{F}} , where {\varphi_{\varepsilon}} perturbation φ. We also prove {\varphi^{*}\mathcal{F}_{\varepsilon}} consist exactly which tangent fibers In order do so, state some results independent interest regarding Kupka these foliations.