on variable and primitive cohomology of a hypersurface in a projective space - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T19:04:19Z http://mathoverflow.net/feeds/question/110568 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/110568/on-variable-and-primitive-cohomology-of-a-hypersurface-in-a-projective-space on variable and primitive cohomology of a hypersurface in a projective space rick 2012-10-24T18:24:39Z 2012-10-24T18:24:39Z <p>I have a smooth hypersurface D in $\mathbb{P}^n$: in many books about Hodge theory (as the ones of Voisin and Carlson) they take for granted that the primitive cohomology of D is equal the variable cohomology of D. (the variable cohomology of D is the ker of the gysin map $\gamma: H^p(D,\mathbb{C}) \rightarrow H^{p+2}(\mathbb{P}^n \setminus X, \mathbb{C})$ ). it must be simple, but i can't see why</p>