Let $X$ be a projective scheme over field $k$, $\mathscr{L}$ be a very ample line bundle on $X$, and $\mathscr{F}$ be a coherent sheaf on $X$.
There is an unique $\mathbb{Q}$-coefficient polynomial $P(X)\in \mathbb{Q}[X]$,
s.t. for $n\in \mathbb{Z}$,
$$P(n)=\chi(\mathscr{F}\otimes \mathscr{L}^{\otimes n}).$$
What is the degree of the polynomial $P(X)$? And is it determined by $X, \mathscr{L}, \mathscr{F}$?
Please tell me hint or reference, thanks.