Rational jet dependence of formal equivalences between real-analytic hypersurfaces in ℂ²

R. Travis Kowalski

Vol. 220 (2005), No. 1, 107–139

DOI: 10.2140/pjm.2005.220.107

Abstract

Let (M,p) and (M,p) be the germs of real-analytic 1-infinite type hypersurfaces in ℂ². We prove that any formal equivalence sending (M,p) into (M,p) is formally parametrized (and hence uniquely determined by) its jet at p of a predetermined order depending only on (M,p). As an application, we use this to examine the local formal transformation groups of such hypersurfaces.

Keywords

real hypersurfaces, formal equivalence, jet determination

Mathematical Subject Classification 2000

Primary: 32H12, 32V20

Milestones

Received: 17 March 2003

Revised: 27 March 2004

Accepted: 12 April 2004

Published: 1 May 2005