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

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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},
     journal = {Sbornik. Mathematics},
     pages = {145--154},
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     volume = {21},
     number = {1},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1973_21_1_a6/}
}
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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/