In this paper we prove that the moduli spaces of framed vector bundles over a surface X, satisfying certain conditions, admit a family of Poisson structures parametrized by the global sections of a certain line bundle on X. This generalizes to the case of framed vector bundles previous results obtained by the author for the moduli space of vector bundles over a Poisson surface. As a corollary of this result we prove that the moduli spaces of framed \SU(r)-instantons on S^4 = R^4 \cup \{\infty\} admit a natural holomorphic symplectic structure.

Poisson Structures on Moduli Spaces of Framed Vector Bundles on Surfaces

BOTTACIN, FRANCESCO
2000

Abstract

In this paper we prove that the moduli spaces of framed vector bundles over a surface X, satisfying certain conditions, admit a family of Poisson structures parametrized by the global sections of a certain line bundle on X. This generalizes to the case of framed vector bundles previous results obtained by the author for the moduli space of vector bundles over a Poisson surface. As a corollary of this result we prove that the moduli spaces of framed \SU(r)-instantons on S^4 = R^4 \cup \{\infty\} admit a natural holomorphic symplectic structure.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/124271
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