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.
Aronszajn, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order
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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.