2009/11/10 by Youssef Alaoui, Alaoui, Youssef
Mathematics · #32E10 #32E40 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.0911.1800
openalex publication_date 2009/11/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
In this article, we prove that if Π: X→ Ω is an unbranched Riemann domain with Ω Stein of dimension n and Π a locally q-complete morphism, then X is cohomologically q-complete if n≥ 3 and 1≤ q≤ n-2 or if Ω has dimension 2 and 1≤ q≤ 2. This generalizes a well-known result which is obtained in ~\citeref3 for q=1 when X and Ω have isolated singularities and, gives in particular a positive answer to the local Steiness problem, namely if X is a Stein space and Ω a locally Stein open subset of X, then Ω is Stein.