Vortex equation and reflexive sheaves

Abstract

It is known that given a stable holomorphic pair $(E,\varphi )$, where $E$ is a holomorphic vector bundle on a compact Kähler manifold $X$ and $\varphi$ is a holomorphic section of $E$, the vector bundle $E$ admits a Hermitian metric solving the vortex equation. We generalize this to pairs $(\E ,ϕ)$, where $\E$ is a reflexive sheaf on $X$.