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arXiv · alg-geom/9505006

Blowups and gauge fields

Nicholas P. Buchdahl
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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 "stabilising" unstable bundles and desingularising moduli of stable bundles; an analysis of the behaviour 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 (using results of a concurrent preprint) that this topology is compact in many cases---i.e., a new compactification for moduli of stable bundles on the original surface.

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BibTeXRIS

Nicholas P. Buchdahl. 1995-05-05. Blowups and gauge fields. https://arxiv.org/abs/alg-geom/9505006

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