Hilbert Coefficients and the Depth of Associated Graded Rings with Respect to Parameter Ideals

  • Cao Huy LinhEmail author
  • Van Duc Trung


In this paper, we investigate the non-positivity for the Hilbert coefficients of parameter ideals. Moreover, we establish a relationship between the vanishing of Hilbert coefficients and the depth of associated graded rings with respect to parameter ideals in the case of small regularity.


Hilbert coefficients The depth of associated graded rings Parameter ideals Castelnuovo–Mumford regularity Postulation number 

Mathematics Subject Classification (2010)

Primary 13D45 13D07 Secondary 14B15 



This paper was written while the first author was visiting Vietnam Institute for Advanced Study in Mathematics. He would like to thank the VIASM for hospitality and financial support.

The authors are grateful to the referees for valuable comments and suggestions which help to create the final version.

Funding Information

Cao Huy Linh and Van Duc Trung are supported by the NAFOSTED of Vietnam under grant number 101.04-2015.32.


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Mathematics, College of EducationHue UniversityHueVietnam

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