The local Torelli theorem for varieties with divisible canonical class

In this paper the local Torelli theorem is proved for a number of varieties with divisible canonical class: surfaces with a family of elliptic curves and base $P^1$, fiberings by varieties with $K=0$ whose base is a curve, complete intersections, cyclic coverings, and surfaces with $V$, $K>0$, $\operatorname{Pic}V=Z$ and $h^{1,0}=0$, whose invariants satisfy certain conditions.
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