On the coniveau of certain sub-Hodge structures
classification
🧮 math.AG
keywords
conjecturehodgecertainconiveaugeneralizedkernelsub-hodgeassuming
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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.
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