Abstract
We investigate the geometry of the Kodaira moduli space M of sections of $$\pi :Z\rightarrow {\mathbb {P}}^1$$ , 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.
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