Regularity comparison of fiber cone and associated graded ring

  • Mousumi Mandal
  • Ramakrishna NanduriEmail author
Original Paper


Let \((A,\mathfrak {m} )\) be a Noetherian local ring and I be an \(\mathfrak {m} \)-primary ideal of A. In this article, we show that if A is a 2-dimensional Buchsbaum local ring and \({\text {depth}}(A)>0\), then \({\text {reg}}(F(I))\le \max \{s^*(\mathcal {F})-2, {\text {reg}}(G(I))\}\) and the equality case is discussed. We also study the upper bounds for \({\text {reg}}(G(\mathbb {M}))\) in terms of multiplicity and Ratliff-Rush closure for 1-dimensional good I-filtrations \(\mathbb {M}\).


Rigidity Buchsbaum ring Castelnuovo-Mumford regularity Good filtration Local cohomology Ratliff-Rush closure 

Mathematics Subject Classification

Primary: 13A30 Secondary: 13C14 13H10 14M05 



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Copyright information

© The Managing Editors 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia

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