Algebraic subellipticity and dominability of blow-ups of affine spaces
| dc.contributor.author | Lárusson, F. | |
| dc.contributor.author | Truong, T. | |
| dc.date.issued | 2017 | |
| dc.description.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. | |
| dc.description.statementofresponsibility | Finnur Larusson, Tuyen Trung Truong | |
| dc.identifier.citation | Documenta Mathematica, 2017; 22(2017):151-163 | |
| dc.identifier.issn | 1431-0635 | |
| dc.identifier.issn | 1431-0643 | |
| dc.identifier.uri | http://hdl.handle.net/2440/111156 | |
| dc.language.iso | en | |
| dc.publisher | Universität Bielefeld | |
| dc.relation.grant | http://purl.org/au-research/grants/arc/DP120104110 | |
| dc.relation.grant | http://purl.org/au-research/grants/arc/DP150103442 | |
| dc.subject | Blow-up; affine space; subelliptic; spray; dominable; strongly dominable; Oka manifold | |
| dc.title | Algebraic subellipticity and dominability of blow-ups of affine spaces | |
| dc.type | Journal article | |
| pubs.publication-status | Published |