In this thesis we study the moduli of holomorphic vector bundles over a non-compact complex space X, which will mainly be of dimension 2 or 3 and which contains a distinguished rational curve ℓ ⊂ X. We will consider the situation in which X is the total space of a holomorphic vector bundle on CP1 and ℓ is the zero section. While the treatment of the problem in this full generality requires the study of complex analytic spaces, it soon turns out that a large part of it reduces to algebraic geometry. In particular, we prove that in certain cases holomorphic vector bundles on X are algebraic. A key ingredient in the description of themoduli are numerical invariants that we associate to each holomorphic vector bundle. Moreover, these invariants provide a local version of the second Chern class. We obtain sharp bounds and existence results for these numbers. Furthermore, we find a new stability condition which is expressed in terms of these numbers and show that the space of stable bundles forms a smooth, quasi-projective variety.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:764175 |
| Date | January 2010 |
| Creators | Koeppe, Thomas |
| Contributors | Gasparim, Elizabeth ; Singer, Michael |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/33315 |
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