Definition 33.35.15. Let $k$ be a field. Let $n \geq 0$. Let $\mathcal{F}$ be a coherent sheaf on $\mathbf{P}^ n_ k$. The function $d \mapsto \chi (\mathbf{P}^ n_ k, \mathcal{F}(d))$ is called the Hilbert polynomial of $\mathcal{F}$.

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