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 suficient conditions under which finite jet dependence, convergence and algebraicity results hold.

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