Théorèmes de dépendance algébrique sur les espaces complexes pseudo-concaves

On the embedding and compactification of q-complete manifolds

“…The results that we need from the theory of pseudoconcave spaces can be summarized in the following TOME 56 (2006), FASCICULE 2 Theorem 1.4 (Andreotti [1], Andreotti and Tomassini [2]). -Let X be a connected p-concave manifold of dimension n, p n − 1.…”

“…, ζ n are holomorphic functions such that ζ 2 (0) · · · ζ n (0) = 0. Since C is singular at 0, we can assume that 2 p 1 < p 2 < p 3 · · · p n ∞ and p 2 = qp 1 + r where 0 < r < p 1 Set ψ 0 (t) = ϕ • ν(t) = ϕ(t p1 , t p2 ζ 2 , . .…”

Absolute Gap-Sheaves and Extensions of Coherent Analytic Sheaves

“…On some open neighborhood U of x in 2 'S can be regarded as a coherent subsheaf of S" for some p (Proposition 9, [1]). It is clear that Slp: is isomorphic to Sm& on U and E"(S, Sv) n U=EP(&) n C/.…”

“…Let 7= Supp F. F and S are both coherent and 'S is torsion-free (Proposition 6, [1]). dim Y^n-l (Proposition 7, [1]). We claim that…”

Un phénomène de Hartogs dans les variétés projectives

“…Let U be an open subset in V such that V \Ū is pseudoconcave in the sense of Andreotti and the boundary of U is connected. Let H be the maximal compact reduced divisor in U (see [3] Proof According to Andreotti's theorem (see [1]), M(Z ) is a finite algebraic extension of M(V ). Let f ∈ M(Z ) be a primitive element.…”