A characterization of rationally convex immersions (Octavian Mitrea - The University of Western Ontario)

Let S be a smooth, totally real, compact immersion in <nobr>Cn</nobr> of real dimension <nobr>m≤n</nobr>, which is locally polynomially convex and it has finitely many points where it self-intersects finitely many times, transversely or non-transversely. Our result proves that S is rationally convex if and only if it is isotropic with respect to a ``degenerate" Kähler form in <nobr>Cn</nobr>. We also show that  there exists a large class of such rationally convex immersions that are not isotropic with respect to any genuine (non-degenerate) Kähler form.