A variation of the reduced Vafa-Witten equations on 4-manifolds

2022/08/12 by Ren Guan, Guan, Ren
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2208.06131

openalex publication_date 2022/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider a variation of the Vafa-Witten equations on compact, oriented and smooth 4-manifolds, and construct a set of perturbation terms to establish the transversality of that equations. The new perturbed equations provide us a priori estimates of the solutions, while the original reduced Vafa-Witten equations does not. By applying the a priori estimates we show that the singular of the solutions can be removed, and then construct the Ulhenbeck closure of the moduli spaces.

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