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For questions on the Hilbert function and Hilbert polynomial of graded algebras over fields.
6
votes
Examples of smooth projective varieties with "nice" Picard group
Here is a simple example. Let $X = P^1 \times Q^3$ and $H = O(1,1)$. The Hilbert polynomial of the line bundle $O(a,b)$ is
$$
P(t) = (t+a+1)(t+b+1)(t+b+2)(t+b+3/2)/3.
$$
It has three integral roots $- …