Polynomial hulls of real manifolds in \(\mathbb C^ 2\) (Q1325637)

Three examples concerning polynomial hulls of some manifolds in \(Bbb C^ 2\) are presented: 1. Some real surfaces with equation \(w= P(z,\bar z)+ G(z)\), where \(P\) is a homogeneous polynomial of degree \(n\) and \(G(z)= o(| z|^ n)\) at \(0\) which are locally polynomially convex at \(0\). 2. Some real surfaces \(M_ F\) with equation \(w= z^{n+k}\bar z^ n+ F(z,\bar z)\) such that the hull of \(M_ F\cap \overline B(0,1)\) contains a neighborhood of \(0\). 3. A countable union of totally real planes \((P_ j)\) such that \(\overline B(0,1)\cap(\bigcup_{j\in N}P_ j)\) is polynomially convex. [Remarks: The review above is almost literary the abstract].