  We consider $\mathcal{N}=2$ supersymmetric pure gauge theories on toric
K\"ahler manifolds, with particular emphasis on $\mathbb{CP}^2$. By choosing a
vector generating a $U(1)$ action inside the torus of the manifold, we
construct equivariantly twisted theories. Then, using localization, we compute
their supersymmetric partition functions. As expected, these receive
contributions from a classical, a one-loop, and an instanton term. It turns out
that the one-loop term is trivial and that the instanton contributions are
localized at the fixed points of the $U(1)$. In fact the full partition
function can be re-written in a factorized form with contributions from each of
the fixed points. The full significance of this is yet to be understood.
