Vortex equation and reflexive sheaves

It is known that given a stable holomorphic pair $(E ,ϕ)$, where $E$ is a holomorphic vector bundle on a compact Kähler manifold $X$ and $ϕ$ 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 $X$.

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