The Stacks project

Exercise 111.45.2. In Situation 111.45.1.

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

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

3. 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 $\mathcal{F}$?