Geodesic
A PERTURBATION AND GENERIC SMOOTHNESS OF THE VAFA–WITTEN MODULI SPACES ON CLOSED SYMPLECTIC FOUR-MANIFOLDS
Glasgow mathematical journal, Tome 61 (2019) no. 2, pp. 471-486

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DOI

We prove a Freed–Uhlenbeck style generic smoothness theorem for the moduli space of solutions to the Vafa–Witten equations on a closed symplectic four-manifold by using a method developed by Feehan for the study of the PU(2)-monopole equations on smooth closed four-manifolds. We introduce a set of perturbation terms to the Vafa–Witten equations, and prove that the moduli space of solutions to the perturbed Vafa–Witten equations on a closed symplectic four-manifold for the structure group SU(2) or SO(3) is a smooth manifold of dimension zero for a generic choice of the perturbation parameters. 
TANAKA, YUUJI. A PERTURBATION AND GENERIC SMOOTHNESS OF THE VAFA–WITTEN MODULI SPACES ON CLOSED SYMPLECTIC FOUR-MANIFOLDS. Glasgow mathematical journal, Tome 61 (2019) no. 2, pp. 471-486. doi: 10.1017/S0017089518000307
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     author = {TANAKA, YUUJI},
     title = {A {PERTURBATION} {AND} {GENERIC} {SMOOTHNESS} {OF} {THE} {VAFA{\textendash}WITTEN} {MODULI} {SPACES} {ON} {CLOSED} {SYMPLECTIC} {FOUR-MANIFOLDS}},
     journal = {Glasgow mathematical journal},
     pages = {471--486},
     year = {2019},
     volume = {61},
     number = {2},
     doi = {10.1017/S0017089518000307},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000307/}
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