A perturbation and generic smoothness of the Vafa-Witten moduli spaces on closed symplectic four-manifolds

Author: 

Tanaka, Y

Publication Date: 

13 July 2018

Journal: 

Glasgow Mathematical Journal

Last Updated: 

2020-03-09T06:25:35.28+00:00

Issue: 

2

Volume: 

61

DOI: 

10.1017/S0017089518000307

page: 

471-486

abstract: 

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.

Symplectic id: 

871237

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article