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I'm learning Yang-Mills theory and its applications on 4-manifold. I want to know that have someone computed all the anti-self-dual connections on principle $SU(2)$ bundles over complex projective space $CP^2$. Where can I find the original paper if someone has calculated it?

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migrated from meta.mathoverflow.net Jun 30 '13 at 13:53

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Donaldson-Kronheimer's book The Geometry of Four-Manifolds computes the moduli space for small 2nd Chern class (it's empty for $c_2=1$); check the examples in chapter 4. But it's not computed by explicitly writing down connections (compared to the $S^4$ scenario). You should be able to find appropriate references there. –  Chris Gerig Jun 30 '13 at 18:26
You also have the Atiyah-Drinfeld-Hitchin-Manin construction en.wikipedia.org/wiki/ADHM_construction, on one side, and twistor space of Atiyah-Hitchin-Singer, or actually and originally R Penrose, on the other, which leads to complex algebraic geometry and results of Horrocks, Barth and Hartshorne. The twistor space of CP2 is the flag manifold F(C3)... –  Albuquerque Dec 16 '13 at 18:23

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