On the Euler-Poincaré characteristic and mixed multiplicities of maximal degrees

2018/03/25 by Thanh, Truong Thi Hong, Viet, Duong Quoc
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.09201

Abstract

This paper defines the Euler-Poincaré characteristic of joint reductions of ideals which concerns the maximal terms in the Hilbert polynomial; characterizes the positivity of mixed multiplicities in terms of minimal joint reductions; proves the additivity and other elementary properties for mixed multiplicities. The results of the paper together with the results of [17] seem to show a natural and nice picture of mixed multiplicities of maximal degrees.

Related

• The Euler-Poincare characteristic and mixed multiplicities
• The Recursion Formula for Mixed Multiplicities with respect to Joint\n Reductions
• Hilbert functions of multigraded algebras, mixed multiplicities of ideals and their applications
• Toward mixed multiplicities and joint reductions
• Positivity of mixed multiplicities