Geodesic
The local Torelli theorem for varieties with divisible canonical class
Izvestiya. Mathematics, Tome 12 (1978) no. 1, pp. 53-67 
K. I. Kii. The local Torelli theorem for varieties with divisible canonical class. Izvestiya. Mathematics, Tome 12 (1978) no. 1, pp. 53-67. http://geodesic.mathdoc.fr/item/IM2_1978_12_1_a2/
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     title = {The local {Torelli} theorem for varieties with divisible canonical class},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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. Bibliography: 7 titles.

[1] Griffiths P. A., “Periods of integrals on algebraic manifolds. II”, Amer. J. Math., 90:3 (1968), 805–866 | DOI | MR

[2] Kii K. I., “Lokalnaya teorema Torelli dlya tsiklicheskikh nakrytii $P^n$ s polozhitelnym kanonicheskim klassom”, Matem. sb., 92:1 (1973), 142–151 | MR | Zbl

[3] Peters C., “The local Torelli theorem. I”, Math. Ann., 217:1 (1975), 1–16 | DOI | MR | Zbl

[4] Bott R., “Homogeneous vector bundles”, Ann. Math., 66:2 (1957), 203–248 | DOI | MR | Zbl

[5] Chzhen Shen-Shen, Kompleksnye mnogoobraziya, IL., M., 1967

[6] Algebraicheskie poverkhnosti, Nauka, M., 1965

[7] Kodaira K., “On compact complex analytic surfaces. I”, Ann. Math., 71:1 (1960), 111–152 | DOI | MR | Zbl