%0 Journal Article
%T On the lengths of quotients of ideals and depths of fiber cones
%A A. V. Jayanthan
%A Ramakrishna Nanduri
%J Mathematics
%D 2009
%I arXiv
%X 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 $\sum_{n\geq0}\lambda(\mathfrak{m}I^{n+1} \cap J/\mathfrak{m}JI^n)$.
%U http://arxiv.org/abs/0906.4649v1