Non-abelian Seiberg-Witten theory and projectively stable pairs

Details Non-abelian Seiberg-Witten theory and projectively stable pairs Non-abelian Seiberg-Witten theory and projectively stable pairs

1996-09-26

arxiv.org/abs/alg-geom/9609020v3

Physics

High Energy Physics

High Energy Physics - Theory

TeX-Type: LaTeX, 31 pages, revised version

Scientific paper

We introduce the concept of Spin^G-structure in a SO-bundle, where $G\subset U(V)$ is a compact Lie group containing $-id_V$. We study and classify $Spin^G(4)$-structures on 4-manifolds, we introduce the G-Monopole equations associated with a $Spin^G$-structure. On Kaehler surfaces a Kobayashi-Hitchin correspondence can be proved for the corresponding moduli spaces. Using this complex geometric interpretation, we determine explicitely a moduli space of "PU(2)-Monopoles" on $\P^2$, we describe its Uhlenbeck compactification, as well as the Donaldson- and the abelian locus.

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