The Euler-Poincare characteristic and mixed multiplicities

The Euler-Poincare characteristic and mixed multiplicities

This paper defines mixed multiplicity systems; the Euler-Poincare characteristic and the mixed multiplicity symbol of $\mathbb{N}^d$-graded modules with respect to a mixed multiplicity system, and proves that the Euler-Poincare characteristic and the mixed multiplicity symbol of any mixed multiplici...

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Bibliographic Details
Main Authors: Viet, Duong Quoc, Thanh, Truong Thi Hong
Format: Journal Article
Language:English
Published: 02-11-2012
Subjects:
Mathematics - Commutative Algebra
Online Access:Get full text
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Summary:This paper defines mixed multiplicity systems; the Euler-Poincare characteristic and the mixed multiplicity symbol of $\mathbb{N}^d$-graded modules with respect to a mixed multiplicity system, and proves that the Euler-Poincare characteristic and the mixed multiplicity symbol of any mixed multiplicity system of the type $(k_1,\ldots,k_d)$ and the $(k_1,\ldots,k_d)$-difference of the Hilbert polynomial are the same. As an application, we get results for mixed multiplicities.
DOI:10.48550/arxiv.1211.1238