On the lengths of quotients of ideals and depths of fiber cones

Details On the lengths of quotients of ideals and depths of fiber cones On the lengths of quotients of ideals and depths of fiber cones

2009-06-25

arxiv.org/abs/0906.4649v1

Mathematics

Commutative Algebra

16 Pages

Scientific paper

Let $(R,\mathfrak{m})$ be a Cohen-Macaulay local ring, $I$ an $\mathfrak{m}$-primary ideal of $R$ and $J$ its minimal reduction. We study the depths of $F(I)$ under certain depth assumptions on $G(I)$ and length condition on quotients of powers of $I$ and $J$, namely $\sum_{n\geq0}\lambda(\mathfrak{m}I^{n+1}/\mathfrak{m}JI^n)$ and $\sum_{n\geq0}\lambda(\mathfrak{m}I^{n+1} \cap J/\mathfrak{m}JI^n)$.

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