CR-MEROMORPHIC EXTENSION AND THE NONEMBEDDABILITY OF THE ANDREOTTI–ROSSI CR STRUCTURE IN THE PROJECTIVE SPACE

Abstract

Let [Formula: see text] be a polynomially convex compact set and let M be a (2p-1) dimensional (p ≥ 2) maximally complex bounded scarred C1 submanifold of [Formula: see text], irreducible in the current sense. According to Harvey–Lawson [14] and Chirka [4], there exists a bounded irreducible analytic set [Formula: see text] such that [M]=±d[T]. In this paper, we prove that every CR-meromorphic map carrying M into a projective manifold V extends to a meromorphic map F:T → V. We extend the notion of CR-meromorphic maps to CR submanifolds of [Formula: see text] and give another proof of our extension theorem which extends to the greater codimensional case. We also apply our extension result to prove a Lewy type extension theorem for CR-meromorphic maps, a Hartogs type theorem in [Formula: see text] and the non embedding of the Andreotti–Rossi CR structure in [Formula: see text].