  A theorem of Weil and Atiyah says that a holomorphic vector bundle $E$ on a
compact Riemann surface $X$ admits a holomorphic connection if and only if the
degree of every direct summand of $E$ is zero. Fix a finite subset $S$ of $X$,
and fix an endomorphism $A(x) \in \text{End}(E_x)$ for every $x \in S$. It is
natural to ask when there is a logarithmic connection on $E$ singular over $S$
with residue $A(x)$ at every $x \in S$. We give a necessary and sufficient
condition for it under the assumption that the residues $A(x)$ are rigid.
