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    On the coniveau of certain sub-Hodge structures

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    We study the generalized Hodge conjecture for certain sub-Hodge structure defined as the kernel of the cup product map with a big cohomology class, which is of Hodge coniveau at least 1. As predicted by the generalized Hodge conjecture, we prove that the kernel is supported on a divisor, assuming the Lefschetz standard conjecture.Comment: 23 pages. V2: Typos corrected. Comments still welcome. To appear in Math.Res.Let
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