Lárusson, F.Truong, T.2018-03-212018-03-212017Documenta Mathematica, 2017; 22(2017):151-1631431-06351431-0643http://hdl.handle.net/2440/111156Little is known about the behaviour of the Oka property of a complex manifold with respect to blowing up a submanifold. A manifold is of Class A if it is the complement of an algebraic subvariety of codimension at least 2 in an algebraic manifold that is Zariski-locally isomorphic to C-n. A manifold of Class A is algebraically subelliptic and hence Oka, and a manifold of Class A blown up at finitely many points is of Class A. Our main result is that a manifold of Class A blown up along an arbitrary algebraic submanifold (not necessarily connected) is algebraically subelliptic. For algebraic manifolds in general, we prove that strong algebraic dominability, a weakening of algebraic subellipticity, is preserved by an arbitrary blow-up with a smooth centre. We use the main result to confirm a prediction of Forster's famous conjecture that every open Riemann surface may be properly holomorphically embedded into C-2.enBlow-up; affine space; subelliptic; spray; dominable; strongly dominable; Oka manifoldJournal article00300772210004118738000062-s2.0-85032370595387031