Stein complements in compact Kähler manifolds

• DOI: 10.1007/s00208-024-02801-3
• Publication Date: 2024-01-28T09:02:08Z
• Authors: Andreas Höring; Thomas Peternell
• Keywords: 32Q28, 32J27, 14R10, 14E30, 14E05; Mathematics - Algebraic Geometry; Mathematics - Complex Variables; FOS: Mathematics; Complex Variables (math.CV); Algebraic Geometry (math.AG)

Given a projective or compact K��hler manifold X and a (smooth) hypersurface Y, we study conditions under which $X \setminus Y$ could be Stein. We apply this in particular to the case when X is the projectivization of the so-called canonical extension of the tangent bundle $T_M$ of a projective manifold M with Y being the projectivization of $T_M$ itself.<br/>31 pages<br/>