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

A. V. Jayanthan, Ramakrishna Nanduri

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 a…