On q-Runge pairs

• Mihnea Coltoiu ^[1]
  1. [1] Institute of Mathematics of the Romanian Academy
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 2, Nº 2, 2003, págs. 231-235
• Idioma: inglés
• Enlaces
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• Resumen

  • We show that the converse of the aproximation theorem of Andreotti and Grauert does not hold. More precisely we construct a 4-complete open subset D \subset \mathbb{C}^6 (which is an analytic complement in the unit ball) such that the restriction map H^3(\mathbb{C}^6,\mathcal{F}) \rightarrow H^3(D, \mathcal{F}) has a dense image for every \mathcal{F} \in Coh(\mathbb{C}^6) but the pair (D, \mathbb{C}^6) is not a 4-Runge pair.