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- W4293342912 abstract "Let $(A,mathfrak{m})$ be a Cohen-Macaulay local ring of dimension $d geq 2$ with infinite residue field and let $I$ be an $mathfrak{m}$-primary ideal. For $0 leq i leq d$ let $I_i$ be the $i^{th}$-coefficient ideal of $I$. Also let $widetilde{I} = I_d$ denote the Ratliff-Rush closure of $A$. Let $G = G_I(A)$ be the associated graded ring of $I$. We show that if $dim H^j_{G_+}(G)^vee leq j -1$ for $1 leq j leq i leq d-1$ then $(I^n)_{d-i} = widetilde{I^n}$ for all $n geq 1$. In particular if $G$ is generalized Cohen-Macaulay then $(I^n)_1 = widetilde{I^n}$ for all $n geq 1$. As a consequence we get that if $A$ is an analytically unramified domain with $G$ generalized Cohen-Macaulay, then the $S_2$-ification of the Rees algebra $ A[It]$ is $bigoplus_{n geq 0} widetilde{I^n}$." @default.
- W4293342912 created "2022-08-27" @default.
- W4293342912 creator A5049108479 @default.
- W4293342912 date "2022-08-25" @default.
- W4293342912 modified "2023-09-27" @default.
- W4293342912 title "On Coefficient ideals" @default.
- W4293342912 doi "https://doi.org/10.48550/arxiv.2208.12147" @default.
- W4293342912 hasPublicationYear "2022" @default.
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