UPPER BOUND FOR THE FIRST  EULER-POINCARÉ CHARACTERISTICS OF KOZUL COMPLEXES RELATIVE TO PARAMETER IDEALS

Phạm Hồng Nam

doi:10.34238/tnu-jst.5367

UPPER BOUND FOR THE FIRST EULER-POINCARÉ CHARACTERISTICS OF KOZUL COMPLEXES RELATIVE TO PARAMETER IDEALS

About this article

Received: 21/12/21 Revised: 25/02/22 Published: 25/02/22

Authors

Pham Hong Nam , TNU - University of Sciences

Abstract

Let be a Noetherian local ring and be a finitely generated -module of dimension Let be a parameter ideal of . Denote by the homology module of the Koszul generated by the system Set and call it the first Euler-Poincaré characteristic of relative to In this paper, we study the upper bound for the first Euler-Poincaré characteristics of relative to the parameter ideal By using the unmixed degree, the multiplicity, and the superficial elements we give the upper bound for given by where are the unmixed degree, the multiplicity of with respect to respectively.

Keywords

Almost p-standard system of parameters; Cohomological degree; Multiplicity; The first Euler-Poincaré characteristics; Unmixed degree

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DOI: https://doi.org/10.34238/tnu-jst.5367

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