Exercise 111.45.2. In Situation 111.45.1.

If $P(t)$ is the Hilbert polynomial of $\mathcal{F}$, what is the Hilbert polynomial of $\mathcal{F}(-13)$.

If $P_ i$ is the Hilbert polynomial of $\mathcal{F}_ i$, what is the Hilbert polynomial of $\mathcal{F}_1 \oplus \mathcal{F}_2$.

If $P_ i$ is the Hilbert polynomial of $\mathcal{F}_ i$ and $\mathcal{F}$ is the kernel of a surjective map $\mathcal{F}_1 \to \mathcal{F}_2$, what is the Hilbert polynomial of $\mathcal{F}$?

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