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# Advances in Theoretical and Mathematical Physics

## Volume 16 (2012)

### Number 2

### Vortex equation and reflexive sheaves

Pages: 713 – 723

DOI: http://dx.doi.org/10.4310/ATMP.2012.v16.n2.a8

#### Authors

#### Abstract

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 $X$.