Algebraic Oka Theory for Curves
| dc.contributor.advisor | Larusson, Finnur | |
| dc.contributor.advisor | Stevenson, Daniel | |
| dc.contributor.author | Dye, Ryan James | |
| dc.contributor.school | School of Mathematical Sciences | en |
| dc.date.issued | 2022 | |
| dc.description.abstract | In 1989, Winkelmann gave a complete classification of the pairs of Riemann surfaces (X, Y ) that satisfy the basic Oka principle (BOP): every continuous map from X into Y is homotopic to a holomorphic one. This thesis is motivated by the analogous problem in the algebraic category. Explicitly, we seek to provide a complete classification of the pairs of smooth algebraic curves that satisfy the basic algebraic Oka principle (aBOP). We give an elementary proof of a special case of Serre’s seminal GAGA principle, which will allow us to translate the problem thus formulated in algebro-geometric terms, into the complex-geometric domain. Here we can use Winkelmann’s result to assist us with our goal. In particular, a pair of smooth algebraic curves cannot satisfy aBOP if it does not satisfy BOP. Finally, we discuss a framework for which the basic algebraic Oka property with approximation can be explored. | en |
| dc.description.dissertation | Thesis (MPhil) -- University of Adelaide, School of Mathematical Sciences, 2022 | en |
| dc.identifier.uri | https://hdl.handle.net/2440/136021 | |
| dc.language.iso | en | en |
| dc.provenance | This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legals | en |
| dc.subject | Complex geometry | en |
| dc.subject | Algebraic Geometry | en |
| dc.subject | Oka Theory | en |
| dc.title | Algebraic Oka Theory for Curves | en |
| dc.type | Thesis | en |
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