Geodesic
$K$-Trivial Structures on Fano Complete Intersections
Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 608-616.

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It is proved that any fiber space structure into varieties of Kodaira dimension zero on a generic Fano complete intersection of index 1 and of dimension $M$ in $\mathbb{P}^{M+k}$ is a pencil of hyperplane sections provided that $M\geqslant 2k+1$. The $K$-trivial structures on the varieties with a pencil of Fano complete intersections are described.
Keywords: Fano complete intersection, $K$-trivial structure, pencil of hyperplane sections. 
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A. V. Pukhlikov. $K$-Trivial Structures on Fano Complete Intersections. Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 608-616. http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a12/

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