Acta Mathematica Vietnamica

, Volume 40, Issue 1, pp 37–60 | Cite as

The Chern Numbers and Euler Characteristics of Modules

  • L. Ghezzi
  • S. Goto
  • J. Hong
  • K. Ozeki
  • T. T. Phuong
  • W. V. Vasconcelos
Article

Abstract

The set of the first Hilbert coefficients of parameter ideals relative to a module—its Chern coefficients—over a local Noetherian ring codes for considerable information about its structure–noteworthy properties such as that of Cohen-Macaulayness, Buchsbaumness, and of having finitely generated local cohomology. The authors have previously studied the ring case. By developing a robust setting to treat these coefficients for unmixed rings and modules, the case of modules is analyzed in a more transparent manner. Another series of integers arise from partial Euler characteristics and are shown to carry similar properties of the module. The technology of homological degree theory is also introduced in order to derive bounds for these two sets of numbers.

Keywords

Hilbert function Hilbert coefficient Parameter ideal Local cohomology Euler characteristic Cohen-Macaulay module Vasconcelos module Generalized Cohen-Macaulay module Buchsbaum module 

Mathematics Subject Classification (2010)

13H10 13H15 13A30 

Notes

Acknowledgments

The first author is partially supported by a grant from the City University of New York PSC-CUNY Research Award Program-44. The second author is partially supported by Grant-in-Aid for Scientific Researches (C) in Japan (19540054). The fourth author is supported by a grant from MIMS (Meiji Institute for Advanced Study of Mathematical Sciences). The fifth author is supported by JSPS Ronpaku (Dissertation of PhD) Program. The last author is partially supported by the NSF

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2014

Authors and Affiliations

  • L. Ghezzi
    • 1
  • S. Goto
    • 2
  • J. Hong
    • 3
  • K. Ozeki
    • 2
  • T. T. Phuong
    • 4
  • W. V. Vasconcelos
    • 5
  1. 1.Department of MathematicsNew York City College of Technology-CunyBrooklynUSA
  2. 2.Department of Mathematics, School of Science and TechnologyMeiji UniversityKawasakiJapan
  3. 3.Department of MathematicsSouthern Connecticut State UniversityNew HavenUSA
  4. 4.Department of Information Technology and Applied MathematicsTon Duc Thang UniversityHo Chi Minh CityVietnam
  5. 5.Department of MathematicsRutgers UniversityPiscatawayUSA

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