  The base space of a semi-universal unfolding of a hypersurface singularity
carries a rich geometric structure, which was axiomatized as a CDV-structure by
C. Hertling. For any CDV-structure on a Frobenius manifold M, the pull-back of
the (1,0)-tangent bundle of M to the product of M by the complex line carries
two natural holomorphic structures equipped with flat meromorphic connections.
We show that, for any semi-simple CDV-structure, there is a formal isomorphism
between these two bundles compatible with connections. Moreover, if we assume
that the super-symmetric index Q vanishes, we give a necessary and sufficient
condition for such a formal isomorphism to be convergent, and we make it
explicit for dim M = 2.
