A Parametric Jet-Interpolation Theorem for Holomorphic Automorphisms of $$\mathbb {C}^n$$

We consider the problem of interpolating a holomorphic family of nondegenerate holomorphic jets on \(\mathbb {C}^n\) for \(n>1\), parametrized by points in a Stein manifold, by a holomorphic family of automorphisms of \(\mathbb {C}^n\). We show that under a suitable topological condition it is possible to find a solution, thereby generalizing results of Forstneric and Varolin concerning the nonparametric jet interpolation by automorphisms.