Un phénomène de Hartogsdans les variétés projectives

Abstract

In this article, we study univalent open subsets U → V , dimV ≥ 2, assuming V \Ū to be pseudoconcave in Andreotti's sense. We prove an Hartogs's Kugelsatz theorem for such open sets : Let U an open subset in V such that V \Ū is a pseudoconcave domain in the sense of Andreotti. Then U contains a maximal compact hypersurface H. Moreover, any meromorphic section s, of a vector bundle F over V , defined on (a neighborhood of) ∂ 0 U extends on U \ H, and, if s is holomorphic then s extends meromorphically to U , with a polar set in H.