Geodesic
A local Torelli theorem for cyclic coverings of $P^n$ with positive canonical class
Sbornik. Mathematics, Tome 21 (1973) no. 1, pp. 145-154 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we prove a local Torelli theorem for cyclic coverings of $P^n$ with $K>0$, and also for varieties which have $K>0$, with $|K|$ having no fixed components and which is not a pencil, $h^{n-1,0}(V)=0$ and $\dim H^0(V,\Omega^{n-1}(K)). Bibliography: 5 titles. 
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     author = {K. I. Kii},
     title = {A~local {Torelli} theorem for cyclic coverings of $P^n$ with positive canonical class},
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K. I. Kii. A local Torelli theorem for cyclic coverings of $P^n$ with positive canonical class. Sbornik. Mathematics, Tome 21 (1973) no. 1, pp. 145-154. http://geodesic.mathdoc.fr/item/SM_1973_21_1_a6/

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[2] P. A. Griffiths, “On the periods of certain rational integrals, I”, Ann. Math., 90:3 (1969), 460–496 | DOI | MR | Zbl

[3] J. Wavric, “Deformations of branched covering of complex manifolds”, Amer. J. Math., 90:3 (1968), 1926–1961

[4] Chzhen Shen-shen, Kompleksnye mnogoobraziya, IL, Moskva, 1961

[5] M. Baldassarri, Algebraicheskie mnogoobraziya, IL, Moskva, 1961 | MR