Holomorphic maps of real submanifolds in complex spaces of different dimensions

Bernhard Lamel

Vol. 201 (2001), No. 2, 357–387

DOI: 10.2140/pjm.2001.201.357

Abstract

We define a new local invariant (called degeneracy) associated to a triple (M,M^′,H), where M ⊂ ℂ^N and M^′⊂ ℂ^N′ are real submanifolds of ℂ^N and ℂ^N′ , respectively, and H : M → M^′ is either a holomorphic map, a formal holomorphic map, or a smooth CR-map. We use this invariant to find sufficient conditions under which finite jet dependence, convergence and algebraicity results hold.

Milestones

Received: 9 November 1999

Revised: 16 June 2000

Published: 1 December 2001