On the Euler-Poincaré characteristic and mixed multiplicities of maximal degrees
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.
arXiv comment22 pages