  Let $n$ be a positive even integer and $d$ a positive integer . To every
complete family $Z$ of n dimensional degree d hypersurfaces in the projective
space with isolated A-D-E singularities we construct according to an idea of
Carlson-Toledo a Deligne-Mumford stack $\bar Z$ whose moduli space is $Z$ such
that the monodromy representation extends. We study the corresponding periods
mapping and establish an infinitesimal Torelli theorem along the isosingular
strata of lZ$ under transversality assumptions. We apply this result to prove
Steiness of the universal covering space of $\bar Z$.
