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• W2080147359 abstract "Griffiths computation of the Hodge filtration on the cohomology of a smooth hypersurface X of degree d in $${mathbb{P}^n}$$ shows that it has coniveau ≥ c once n ≥ dc. The generalized Hodge conjecture (GHC) predicts that the cohomology of X is then supported on a closed algebraic subset of codimension at least c. This is essentially unknown for c ≥ 2. In the case where c = 2, we exhibit a geometric phenomenon in the variety of lines of X explaining the estimate for the coniveau, and show that (GHC) would be implied in this case by the following conjecture on effective cones of cycles of intermediate dimension: Very moving subvarieties have their class in the interior of the effective cone." @default.
• W2080147359 created "2016-06-24" @default.
• W2080147359 creator A5068122125 @default.
• W2080147359 date "2009-12-10" @default.
• W2080147359 modified "2023-10-13" @default.
• W2080147359 title "Coniveau 2 Complete Intersections and Effective Cones" @default.
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• W2080147359 doi "https://doi.org/10.1007/s00039-009-0036-0" @default.
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