In Remark 4.8 we noted that the case where $n=0$ and $m_{j}=2$ for all $j=1,\dots,8$ reduces to the usual Kummer construction. Hence we know that $M_{\epsilon}$ is diffeomorphic to the K3 surface in this special case. It seems likely one can prove that the diffeomorphism type of $M_{\epsilon}$ does not depend on the configuration of punctures satisfying the balancing condition (4.1). Since we are going to construct a hyperkähler metric on $M_{\epsilon}$, the calculation of the Betti numbers will anyway imply that $M_{\epsilon}$ is always diffeomorphic to the K3 surface.