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

2010/02/24 by Clare D'Cruz, D'Cruz, Clare
Mathematics · #13A02 #13C15 #13H10 #13H15 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A02 #msc:13C15 #msc:13H10 #msc:13H15

paper · pdf · doi:10.48550/arxiv.1002.4466

arxiv created 2010/02/24 · arxiv updated 2010/02/26

Abstract

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) ≥ d- 1 implies that \depth F(I) ≥ 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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