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I am trying to compute the number of section of the restriction of the line bundle $O(m)$ to a hyper-surface $V$, given by a degree $d$ polynomial. I cannot figure out how to do this and any help would be appreciated.

Pax
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    I assume you meant $m$ and not $n$ for the twist and $n\geq 2$. You have an exact sequence, $0\to\mathcal{O}{\mathbb{P}^n}(-d)\to \mathcal{O}{\mathbb{P}^n}\to\mathcal{O}V\to 0$. Thus, we get $h^0(\mathcal{O}_V(m))=h^0(\mathcal{O}{\mathbb{P}^n}(m))-h^0(\mathcal{O}_{\mathbb{P}^n}(m-d))$, which I am sure you know how to calculate. – Mohan Nov 16 '16 at 23:40
  • @Mohan I have correct it thanks. Now we can just use $h^0(\mathcal{O}_{\mathbb{P}^n}(m))=\binom{n+m}{m}$? – Pax Nov 16 '16 at 23:55
  • I've answered a similar question here. – Fredrik Meyer Nov 17 '16 at 11:35
  • @GeorgesElencwajg Thank you. I had specifically said that I am assuming $n\geq 2$ in my answer. Beginners get flustered when one invokes higher cohomologies, so I avoided it. – Mohan Nov 17 '16 at 13:25

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