Geodesic
Algebraic Subellipticity and Dominability of Blow-Ups of Affine Spaces
Documenta mathematica, Tome 22 (2017), pp. 151-163.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 $\Cal A$ if it is the complement of an algebraic subvariety of codimension at least 2 in an algebraic manifold that is Zariski-locally isomorphic to $\Bbb C^{n}$. A manifold of Class $\Cal A$ is algebraically subelliptic and hence Oka, and a manifold of Class $\Cal A$ blown up at finitely many points is of Class $\Cal A$. Our main result is that a manifold of Class $\Cal A$ 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 $\Bbb C^{2}$.
Classification : 14R10, 32S45, 32Q99, 14M20
Keywords: blow-up, affine space, subelliptic, strongly dominable, Oka manifold 
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Lárusson, Finnur; Truong, Tuyen Trung. Algebraic Subellipticity and Dominability of Blow-Ups of Affine Spaces. Documenta mathematica, Tome 22 (2017), pp. 151-163. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a47/