An abelian gauge-theoretic variant of the Seiberg-Witten equations for multiple-spinors

2023/01/23 by Minh Lam Nguyen, Nguyen, Minh Lam
Mathematics · #53C07 #53C27 #53C80 #57R57 #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2301.09693

openalex publication_date 2023/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a variant of the Seiberg-Witten equations for multiple-spinors. The moduli space of solutions to our generalized Seiberg-Witten equations in the setting of Kähler surfaces has a direct relation with ASD connections of holomorphic vector bundle. Also in Kähler setting, we construct a numerical invariant from the equations that detects a notion of ϕ-stability of SU(n)-holomorphic vector bundles where ϕ is some prescribed non-trivial holomorphic section.

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