De Paepe’s disc has nontrivial polynomial hull

• Autores: Anthony G. O'Farrell, M. A. Sanabria-Garcia
• Localización: Bulletin of the London Mathematical Society, ISSN 0024-6093, Vol. 34, Nº 4, 2002, págs. 490-494
• Idioma: inglés
• DOI: 10.1112/s0024609302001108
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• Resumen

  • 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.