2021/06/25 by Ankit Mishra, Tony J. Puthenpurakal, Mishra, Ankit +1
Mathematics · #13C15 #13H10 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13A30 #Secondary 13D40
paper · pdf · doi:10.48550/arxiv.2106.13758
openalex publication_date 2021/06/25 · openalex created_date 2023/04/23 · openalex updated_date 2026/07/28
Let (A,\mathfrakm) be a hypersurface ring with dimension d, and M a MCM A-module with red(M)≤ 2 and μ(M)=2 or 3 then we have proved that depth G(M)≥ d-μ(M)+1. If e(A)=3 and μ(M)=4 then in this case we have proved that depthG(M)≥ d-3. Next we consider the case when e(M)=μ(M)i(M)+1 and prove that depth G(M)≥ d-1. When A = Q/(f) where Q = k[[X1,⋯, Xd+1]] then we give estimates for \depth G(M) in terms of a minimal presentation of M. Our paper is the first systematic study of depth of associated graded modules of MCM modules over hypersurface rings.