2022/08/04 by Mishra, Ankit, Puthenpurakal, Tony J.
#13C15 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13A30 #Secondary 13D40
paper · doi:10.48550/arxiv.2208.02667
Let A=Q/(f) where (Q,\mathfrakn) be a complete regular local ring of dimension d+1, f∈ \mathfrakni∖\mathfrakni+1 for some i≥ 2 and M an MCM A-module with e(M)=μ(M)i(M)+1 then we prove that depth G(M)≥ d-1. If (A,\mathfrakm) is a complete hypersurface ring of dimension d with infinite residue field and e(A)=3, let M be an MCM A-module with μ(M)=2 or 3 then we prove that depth G(M)≥ d-μ(M)+1. Our paper is the first systematic study of depth of associated graded modules of MCM modules over hypersurface rings.