Geodesic
A Remark on the Nonrationality Problem for Generic Cubic Fourfolds
Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 61-68.

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It is proved that the nonrationality of a generic cubic fourfold follows from a conjecture on the nondecomposability in the direct sum of nontrivial polarized Hodge structures of the polarized Hodge structure on transcendental cycles on a projective surface.
Keywords: nonrationality problem, generic cubic fourfold, nondecomposability conjecture, polarized Hodge structure, projective surface. 
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Vik. S. Kulikov. A Remark on the Nonrationality Problem for Generic Cubic Fourfolds. Matematičeskie zametki, Tome 83 (2008) no. 1, pp. 61-68. http://geodesic.mathdoc.fr/item/MZM_2008_83_1_a6/

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