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. 
@article{MZM_2012_91_4_a12,
     author = {A. V. Pukhlikov},
     title = {$K${-Trivial} {Structures} on {Fano} {Complete} {Intersections}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {608--616},
     publisher = {mathdoc},
     volume = {91},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a12/}
}
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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/