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Acta Mathematica Vietnamica

, Volume 43, Issue 1, pp 67–81 | Cite as

Stability of Depth and Cohen-Macaulayness of Integral Closures of Powers of Monomial Ideals

  • Le Tuan Hoa
  • Tran Nam Trung
Article
  • 73 Downloads

Abstract

Let I be a monomial ideal in a polynomial ring \(R = k[x_{1},\dots ,x_{r}]\). In this paper, we give an upper bound on \(\overline {\text {dstab}} (I)\) in terms of r and the maximal generating degree d(I) of I such that \(\text {depth} R/\overline {I^{n}}\) is constant for all \(n\geqslant \overline {\text {dstab}}(I)\). As an application, we classify the class of monomial ideals I such that \(\overline {I^{n}}\) is Cohen-Macaulay for some integer n ≫ 0.

Keywords

Depth Monomial ideal Simplicial complex Integral closure 

Mathematics Subject Classification (2010)

13D45 05C90 

Notes

Acknowledgements

This work is partially supported by NAFOSTED (Vietnam) under the grant number 101.04-2015.02.

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Institute of MathematicsVASTHanoiVietnam

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