A parametric jet-interpolation theorem for holomorphic automorphisms of C^n

TL;DR

This paper extends the theory of holomorphic automorphisms of complex n-space by establishing a parametric jet-interpolation theorem, allowing the interpolation of holomorphic jet families by automorphisms under certain topological conditions.

Contribution

It generalizes previous nonparametric jet interpolation results to parametric families, broadening the scope of automorphism interpolation in complex analysis.

Findings

Established a parametric jet-interpolation theorem for holomorphic automorphisms of C^n.

Generalized results of Forstneric and Varolin to the parametric setting.

Provided conditions under which holomorphic families of jets can be interpolated by automorphisms.

Abstract

We consider the problem of interpolating a holomorphic family of nondegenerate holomorphic jets on C^n for n > 1, parametrized by points in a Stein manifold, by a holomorphic family of automorphisms of 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.