  We investigate the geometry of the Kodaira moduli space $M$ of sections of
$\pi:Z\to {\mathbb P}^1$, the normal bundle of which is allowed to jump from
${\mathcal O}(1)^{n}$ to ${\mathcal O}(1)^{n-2m}\oplus {\mathcal
O}(2)^{m}\oplus {\mathcal O}^{m}$. In particular, we identify the natural
assumptions which guarantee that the Obata connection of the hypercomplex part
of $M$ extends to a logarithmic connection on $M$.
