  We discuss the existence of equilibrium configurations for the Hamiltonian
point-vortex model on a closed surface $\Sigma$. The topological properties of
$\Sigma$ determine the occurrence of three distinct situations, corresponding
to $\mathbb{S}^2$, to $\mathbb{RP}^2$ and to $\Sigma
\not=\mathbb{S}^2,\mathbb{RP}^2$. As a by-product, we also obtain new existence
results for the singular mean-field equation with exponential nonlinearity.
