Vortex equation and reflexive sheaves (Q1951478)

Given a stable holomorphic pair \((E,\phi)\), where \(E\) is a holomorphic vector bundle on a compact Kähler manifold \(X\) and \(\phi\) is a holomorphic section of \(E\), the vector bundle \(E\) admits a Hermitian metric solving the vortex equation. This is generalized to pairs \((\mathcal{E},\phi)\), where \(\mathcal{E}\) is a reflexive sheaf on \(X\), see also [\textit{S. B. Bradlow}, Commun. Math. Phys. 135, No. 1, 1--17 (1990; Zbl 0717.53075); \textit{G. Tian} and \textit{B. Yang}, J. Reine Angew. Math. 553, 17--41 (2002; Zbl 1022.53025)].