Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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

share|improve this question
What is $X$ here? –  Craig Westerland Oct 24 '12 at 23:04
i'm sorry, i meant D –  rick Oct 25 '12 at 1:25

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.