Algebraic Subellipticity and Dominability of Blow-Ups of Affine Spaces
Finnur LárussonSchool of Mathematical Sciences, University of Adelaide, Adelaide SA 5005, Australia
Tuyen Trung TruongSchool of Mathematical Sciences, University of Adelaide, Adelaide SA 5005, Australia
Little 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 if it is the complement of an algebraic subvariety of codimension at least 2 in an algebraic manifold that is Zariski-locally isomorphic to . A manifold of Class is algebraically subelliptic and hence Oka, and a manifold of Class blown up at finitely many points is of Class . Our main result is that a manifold of Class 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 .
Cite this article
Finnur Lárusson, Tuyen Trung Truong, Algebraic Subellipticity and Dominability of Blow-Ups of Affine Spaces. Doc. Math. 22 (2017), pp. 151–163DOI 10.4171/DM/562