Equivalences of real submanifolds in complex space.

Abstract

We show that for any real-analytic submanifold M in CN there is a proper real-analytic subvariety V contained in M such that for any p ? M \ V , any real-analytic submanifold M? in CN, and any p? ? M?, the germs of the submanifolds M and M? at p and p? respectively are formally equivalent if and only if they are biholomorphically equivalent. More general results for k-equivalences are also stated and proved.