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Instantons, Poisson structures and generalized Kaehler geometry

Nigel Hitchin
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Abstract

Using the idea of a generalized Kaehler structure, which is a pair of commuting generalized complex structures, we construct bihermitian metrics on the projective plane and the product of two projective lines, and show that any such structure on a compact 4-manifold M defines one on the moduli space of anti-self-dual connections on a fixed principal bundle over M. We highlight the role of holomorphic Poisson structures in all these constructions.

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Nigel Hitchin. 2005-03-21. Instantons, Poisson structures and generalized Kaehler geometry. https://doi.org/10.1007/s00220-006-1530-y

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