For generic perturbation parameter, the full-rank part of the perturbed Vafa-Witten moduli space is a smooth, oriented, zero-dimensional manifold for SU(2) or SO(3) bundles.
Guan, Transversality of the perturbed reduced Vafa-Witten moduli spaces on 4-manifolds, Differ
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A simple perturbation of Vafa-Witten equations and a transversality result
For generic perturbation parameter, the full-rank part of the perturbed Vafa-Witten moduli space is a smooth, oriented, zero-dimensional manifold for SU(2) or SO(3) bundles.