Blowups and gauge fields
Date
2000
Authors
Buchdahl, N.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
Pacific Journal of Mathematics, 2000; 196(1):69-111
Statement of Responsibility
Conference Name
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.