## Advances in Theoretical and Mathematical Physics

### Vortex equation and reflexive sheaves

#### Abstract

It is known that 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. We generalize this to pairs $(E,\phi)$, where $E$ is a reflexive sheaf on $X$.

#### Article information

Source
Adv. Theor. Math. Phys., Volume 16, Number 2 (2012), 713-723.

Dates
First available in Project Euclid: 23 January 2013