Geodesic
Algebraic Subellipticity and Dominability of Blow-Ups of Affine Spaces
Documenta mathematica, Tome 22 (2017), pp. 151-163
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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 Cn. 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 C2.
DOI : 10.4171/dm/562
Classification : 14M20, 14R10, 32Q99, 32S45
Mots-clés : blow-up, Oka manifold, affine space, subelliptic, strongly dominable 
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     author = {Tuyen Trung Truong and Finnur L\'arusson},
     title = {Algebraic {Subellipticity} and {Dominability} of {Blow-Ups} of {Affine} {Spaces}},
     journal = {Documenta mathematica},
     pages = {151--163},
     year = {2017},
     volume = {22},
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Tuyen Trung Truong; Finnur Lárusson. Algebraic Subellipticity and Dominability of Blow-Ups of Affine Spaces. Documenta mathematica, Tome 22 (2017), pp. 151-163. doi: 10.4171/dm/562

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