Resumen de De Paepe’s disc has nontrivial polynomial hull

Anthony G. O'Farrell, M. A. Sanabria-Garcia

• We show that the topological disc (De Paepe’s) P = {(z2, z¯2 +z¯3): |z| ≤ 1} ⊂ C2 has non-trivial polynomially-convex hull. In fact, we show that this holds for all discs of the form X = {(z2, f(¯z)): |z| ≤ r}, where f is holomorphic on |z| ≤ r, and f(z) = z2 +a3z3 +· · · , with all coefficients an real, and at least one a2n+1 ≠ 0.