Vanishing of cohomology groups - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T19:15:30Z http://mathoverflow.net/feeds/question/105033 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/105033/vanishing-of-cohomology-groups Vanishing of cohomology groups Naga Venkata 2012-08-19T11:30:46Z 2012-08-20T00:57:28Z <p>Given a smooth hypersurface $X \subset \mathbb{P}^{2p+1}_{\mathbb{C}}$ of degree $d \ge 5$ (with $p\ge 2$), when can we say that</p> <p>$H^{p+1}(\mathcal{O}_X)=H^{p+1}(\Omega^1_X)=...=H^{p+1}(\Omega^{p-2}_X)=0$ ?</p> <p>Are there some examples of such a hypersurface? Any suggestions on a possible direction of approaching this problem is more than welcome.</p>