Let R be a finitely N-graded algebra over a Noetherian ring. In this paper we study the asymptotic behaviour of the so called v-number wP(JnM/InN) as function of n where N⊂M are finitely generated R-modules, and I1⊂J1,…,Ir⊂Jr are homogeneous ideals. We prove that wP(M/InN) and wP(InM/In+1–N) are eventually the minimum of r liner functions.
A theorem on the asymptotic behaviour of the generalised v-number
Luca Fiorindo
2024-01-01
Abstract
Let R be a finitely N-graded algebra over a Noetherian ring. In this paper we study the asymptotic behaviour of the so called v-number wP(JnM/InN) as function of n where N⊂M are finitely generated R-modules, and I1⊂J1,…,Ir⊂Jr are homogeneous ideals. We prove that wP(M/InN) and wP(InM/In+1–N) are eventually the minimum of r liner functions.
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