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https://hdl.handle.net/2440/3734
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Type: | Journal article |
Title: | Blowups and gauge fields |
Author: | Buchdahl, N. |
Citation: | Pacific Journal of Mathematics, 2000; 196(1):69-111 |
Publisher: | Pacific Journal Mathematics |
Issue Date: | 2000 |
ISSN: | 0030-8730 |
Abstract: | The relationship between stable holomorphic vector bundles on a compact complex surface and the same such objects on a blowup of the surface is investigated, where "stability" is with respect to a Gauduchon metric on the surface and naturally derived such metrics on the blowup. The main results are: descriptions of holomorphic vector bundles on a blowup; conditions relating (semi)-stability of these to that of their direct images on the surface; sheaf-theoretic constructions for "stabilizing" unstable bundles and desingularising moduli of stable bundles; an analysis of the behavior of Hermitian-Einstein connections on bundles over blowups as the underlying Gauduchon metric degenerates; the definition of a topology on equivalence classes of stable bundles on blowups over a surface and a proof that this topology is compact in many cases. |
DOI: | 10.2140/pjm.2000.196.69 |
Published version: | http://dx.doi.org/10.2140/pjm.2000.196.69 |
Appears in Collections: | Aurora harvest 6 Pure Mathematics publications |
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