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arXiv · 1211.1238

The Euler-Poincare characteristic and mixed multiplicities

Duong Quoc Viet·Truong Thi Hong Thanh
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Abstract

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.

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Duong Quoc Viet, Truong Thi Hong Thanh. 2012-11-03. The Euler-Poincare characteristic and mixed multiplicities. https://arxiv.org/abs/1211.1238

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