= Local cone at an unobstructed reducible SU2 instanton
{title2=$\mathbb C^{4k-1}/S^1$}
On a simply connected negative-definite four-manifold, an ASD connection of full circle holonomy has $h_A^0=1$. If $h_A^2=0$, the index formula gives $h_A^1=8k-2$. The neutral diagonal deformation space vanishes because $b_1=0$, leaving a complex vector space of dimension $4k-1$ with stabilizer action $z\mapsto\lambda^2z$. Kuranishi reduction and the Coulomb slice give the local quotient $\mathbb C^{4k-1}/S^1$, equivalently the cone on $\mathbb{CP}^{4k-2}$.
// Destination: geometry-and-topology.bigb
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