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Cubic fourfolds fibered in sextic del Pezzo surfaces

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arxiv 1606.05321 v4 pith:ONHX67D6 submitted 2016-06-16 math.AG

classification math.AG
keywords rationalcubicexamplesfiberedfourfoldspezzosexticsurfaces
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We exhibit new examples of rational cubic fourfolds, parametrized by a countably infinite union of codimension-two subvarieties in the moduli space. Our examples are fibered in sextic del Pezzo surfaces over the projective plane; they are rational whenever the fibration has a rational section.

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  1. A remark on algebraic cycles on cubic fourfolds

    math.AG 2019-08 reject novelty 4.0 of 10

    The note claims a description of A1 for cubic fourfolds in terms of zero-cycles on surfaces and a resulting non-rationality criterion, but the main theorem is unstated and the proof is internally inconsistent.

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