Approximation and the Topology of Rationally Convex Sets

Zeron, E. S.

Canadian mathematical bulletin, Tome 49 (2006) no. 4, pp. 628-636

Résumé

Considering a mapping $g$ holomorphic on a neighbourhood of a rationally convex set $K\subset {{\mathbb{C}}^{n}}$ , and range into the complex projective space $\mathbb{C}{{\mathbb{P}}^{m}}$ , the main objective of this paper is to show that we can uniformly approximate $g$ on $K$ by rational mappings defined from ${{\mathbb{C}}^{n}}$ into $\mathbb{C}{{\mathbb{P}}^{m}}$ . We only need to ask that the second Čech cohomology group ${{\overset{\scriptscriptstyle\smile}{H}}^{2}}\left( K,\mathbb{Z} \right)$ vanishes.

Détail

DOI : 10.4153/CMB-2006-058-2

Mots-clés : 32E30, 32Q55, Rationally convex, cohomology and homotopy