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For questions on the Hilbert function and Hilbert polynomial of graded algebras over fields.
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On the degree of the Hilbert polynomial of a graded module over the Rees algebra
If $A=\oplus_{n=0}^\infty A_n$ is a Noetherian graded ring of finite dimension such that $A_0$ is local and $A=A_0[A_1]$, and if $M=\oplus_{n=0}^\infty M_n$ is a finitely generated graded $A$-module …