Moduli spaces of framed instanton bundles on CP^3 and twistor sections of moduli spaces of instantons on C^2

Details Moduli spaces of framed instanton bundles on CP^3 and twistor sections of moduli spaces of instantons on C^2 Moduli spaces of framed instanton bundles on CP^3 and twistor sections of moduli spaces of instantons on C^2

2010-06-02

arxiv.org/abs/1006.0440v3

Adv. Math. 227 (2011), 1526-1538

Mathematics

Algebraic Geometry

v. 3.0, 15 pages, many small corrections, thanks to the referee

Scientific paper

We show that the moduli space $M$ of holomorphic vector bundles on $CP^3$ that are trivial along a line is isomorphic (as a complex manifold) to a subvariety in the moduli of rational curves of the twistor space of the moduli space of framed instantons on $\R^4$, called the space of twistor sections. We then use this characterization to prove that $M$ is equipped with a torsion-free affine connection with holonomy in $Sp(2n,\C)$.

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