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arxiv: math/0610963 · v1 · submitted 2006-10-31 · 🧮 math.AG

A remark on the non-rationality Problem for generic cubic fourfolds

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keywords cubicgenerichodgenon-rationalitypolarizedconjecturecyclesdirect
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It is proved that the non-rationality of a generic cubic fourfold follows from a conjecture on the non-decomposability in the direct sum of non-trivial polarized Hodge structures of the polarized Hodge structure on transcendental cycles on a projective surface.

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