Finite jet determination for biholomorphisms of real-analytic hypersurfaces in $C^{N}

Abstract

We prove that for real-analytic hypersurfaces $M$ in $C^{N}$, finite jet determination for biholomorphisms of $M$ holds under minimal assumptions on the geometry of $M$, in both the infinite type and in the finite type cases. In the finite type case, we extend from $N=2$ to arbitrary $N$ a result of Ebenfelt, Lamel and Zaitsev on 2-jet determination of such biholomorphisms.