  Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily
connected, with Lie algebra $g$, endowed with an adjoint action invariant
scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and
pick a Riemannian metric and orientation on $\Sigma$, so that the corresponding
Yang-Mills equations $$d_A*K_A = 0$$ are defined, where $K_A$ refers to the
curvature of a connection $A$. For every central Yang-Mills connection $A$, the
data induce a structure of unitary representation of the stabilizer $Z_A$ on
the first cohomology group $\roman H^1_A(\Sigma,\roman{ad}(\xi))$ with
coefficients in the adjoint bundle $\roman{ad}(\xi)$, with reference to $A$,
with momentum mapping $\Theta_A$ from $\roman H^1_A(\Sigma,\roman{ad}(\xi))$ to
the dual $z^*_A$ of the Lie algebra $z_A$ of $Z_A$. We show that, for every
central Yang-Mills connection $A$, a suitable Kuranishi map identifies a
neighborhood of zero in the Marsden-Weinstein reduced space $\roman H_A$ for
$\Theta_A$ with a neighborhood of the point $[A]$ in the moduli space of
central Yang-Mills connections on $\xi$.
