Tokyo Journal of Mathematics

On the Multiplicity of Multigraded Modules Over Artinian Local Rings

Nguyen Tien MANH and Duong Quoc VIET

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Abstract

Let $S$ be a finitely generated standard multigraded algebra over an Artinian local ring $A$; $M$ a finitely generated multigraded $S$-module. This paper first investigates the relationship between the multiplicity and mixed multiplicities of $M$. Next, we give some applications to multigraded fiber cones.

Article information

Source
Tokyo J. Math., Volume 33, Number 2 (2010), 341-360.

Dates
First available in Project Euclid: 31 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1296483474

Digital Object Identifier
doi:10.3836/tjm/1296483474

Mathematical Reviews number (MathSciNet)
MR2779261

Zentralblatt MATH identifier
1217.13010

Subjects
Primary: 13H15: Multiplicity theory and related topics [See also 14C17]
Secondary: 13A02: Graded rings [See also 16W50] 13E05: Noetherian rings and modules 13E10: Artinian rings and modules, finite-dimensional algebras 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]

Citation

VIET, Duong Quoc; MANH, Nguyen Tien. On the Multiplicity of Multigraded Modules Over Artinian Local Rings. Tokyo J. Math. 33 (2010), no. 2, 341--360. doi:10.3836/tjm/1296483474. https://projecteuclid.org/euclid.tjm/1296483474


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References

  • P. B. Bhattacharya, The Hilbert function of two ideals, Proc. Cambridge. Philos. Soc. 53 (1957), 568–575.
  • C. D'Cruz, A formula for the multiplicity of the multigraded extended Rees algebras, Comm. Algebra. 31 (6)(2003), 2573–2585.
  • M. Herrmann, E. Hyry, J. Ribbe, Z. Tang, Reduction numbers and multiplicities of multigraded structures, J. Algebra 197 (1997), 311–341.
  • D. Katz, J. K. Verma, Extended Rees algebras and mixed multiplicities, Math. Z. 202 (1989), 111–128.
  • N. T. Manh and D. Q. Viet, On the mixed multiplicities of multi-graded fiber cones, Tokyo J. Math. 31 (2008), no. 2, 399–414.
  • P. Roberts, Local Chern classes, multiplicities and perfect complexes, Memoire Soc. Math. France 38 (1989), 145–161.
  • J. K. Verma, Rees algebras and mixed multiplicities, Proc. Amer. Mat. Soc. 104 (1988), 1036–1044.
  • J. K. Verma, Multigraded Rees algebras and mixed multiplicities, J. Pure and Appl. Algebra 77 (1992), 219–228.