Extension of CR mappings between generic algebraic submanifolds

In this thesis we present an extension theorem for CR mappings between generic algebraic submanifolds of CN . Suppose M and M' are generic algebraic submanifolds of CN , of equal dimension, with M connected and holomorphically nondegenerate. It is well known that every holomorphically nondegenerate hypersurface must have points at which it is of finite type. However, this need not be the case for generic submanifolds of higher codimension. Therefore, we also assume that the set of points at which M is of finite type is nonempty. With M and M' as described, we demonstrate that any smooth CR mapping H : M → M', whose Jacobian is not identically zero, extends holomorphically to a neighbourhood of M.