DEFORMATIONS OF CR MAPS AND APPLICATIONS

Abstract

We study the deformation theory of CR maps in the positive codimensional case. In particular, we study structural properties of the mapping locus E of (germs of nondegenerate) holomorphic maps H: (M, p) → M' between generic real submanifolds M ⊂ CN and M ⊂ CN, defined to be the set of points p'∈ M'which admit such a map with H(p) = p. We show that this set E is semi-analytic and provide examples for which E possesses (prescribed) singularities. © 2021. International Press