Hilbert polynomial

《incompressible-fluid-equations》 · 第 165 页 · Proposition 13.2

Let $X\subseteq\mathbb P^n$ be a variety, $h_X$ its Hilbert function. Then there exists a polynomial $p_X$ such that for all sufficiently large $m$, $h_X(m)=p_X(m)$; the degree of the polynomial $p_X$ is the dimension of $X$. The polynomial $p_X$ is called the Hilbert polynomial of $X$.