On the depth of blow-up rings of ideals of minimal mixed multiplicity

Details On the depth of blow-up rings of ideals of minimal mixed multiplicity On the depth of blow-up rings of ideals of minimal mixed multiplicity

2010-02-24

arxiv.org/abs/1002.4466v1

Mathematics

Commutative Algebra

Scientific paper

We show that if $(R, \m)$ is a Cohen-Macaulay local ring and $I$ is an ideal of minimal mixed multiplicity, then $\depth G(I) \geq d- 1$ implies that $\depth F(I) \geq d-1$. We use this to show that if $I$ is a contracted ideal in a two dimensional regular local ring then $\depth R[It]-1= \depth G(I) = \depth F(I)$. We also give an infinite class of ideals where $R[It]$ is Cohen-Macaulay but $F(I)$ is not.

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