Let $f\in R=k[x,y,z]_{(x,y,z)}$ be a homogeneous polynomial of degree $d$, monic in $x$. Show that $(y,z)$ is an ideal of finite colength on $M=R/(f)$. Compute the corresponding Hilbert-Samuel function.
Maybe someone can do it as an example.
2026-03-28 15:19:03.1774711143
Compute the Hilbert-Samuel function
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