Algebraic subellipticity and dominability of blow-ups of affine spaces
Date
2017
Authors
Lárusson, F.
Truong, T.
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Advisors
Journal Title
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Volume Title
Type:
Journal article
Citation
Documenta Mathematica, 2017; 22(2017):151-163
Statement of Responsibility
Finnur Larusson, Tuyen Trung Truong
Conference Name
Abstract
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 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.