Let $X = \mathbb{P}^n_k$ be a projective space over an algebraically closed field $k$ and $x$ be a closed point.

Given an integer $m$ and a positive integer $r$.

What are the global sections of $\mathcal{O}_X(m) \otimes \mathcal{I}_x^r$ where $\mathcal{I}_x$ is the ideal sheaf of $x$ ?

Or what is the dimension of $\Gamma(X,\mathcal{O}_X(m) \otimes \mathcal{I}_x^r)$ ?

`$h^0(\mathbb{P}^2,\mathcal{O}(1)/\mathcal{I}_x^3\mathcal{O}(1))$`

. The dimension should be $6$, not $3$. – Jason Starr May 4 '13 at 20:07