Resumen de Analytic stability of the CR cross-cap

Adam Coffman

• For m < n, any real analytic m-submanifold of complex n-space with a nondegenerate CR singularity is shown to be locally equivalent, under a holomorphic coordinate change, to a fixed real algebraic variety defined by linear and quadratic polynomials. The situation is analogous to Whitney¿s stability theorem for cross-cap singularities of smooth maps. The complex analyticity of the normalizing transformation is proved using a rapid convergence argument.