dd-sequences and partial Euler-Poincare' characteristics of Koszul complex

混合 Koszul 复形的 Euler 示性数与向量场的指数

Euler characteristic of a mixed Koszul complex and the index of vector fields

该研究建立了局部环上三项自由模复形对应的混合 Koszul 复形的 Euler 示性数与混合重数的关系，并将其应用于给出孤立完全交奇点处全纯向量场指数的简单公式。

关于 de Rham 上同调与分次局部上同调模的 Koszul 上同调的欧拉示性数之间关系

On a Relation between Euler characteristics of \MakeLowercase{de} Rham cohomology and Koszul cohomology of graded local cohomology modules

本文证明在特征零域上，分次局部上同调模的 de Rham 上同调与 Koszul 上同调的欧拉示性数满足符号关系 $χ^c(\partial, M) = (-1)^{n+1}χ^c(X, M)$。

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 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.

On the regularity and Koszulness of modules over local rings

Koszul modules over Noetherian local rings $R$ were introduced by Herzog and Iyengar and they possess good homological properties, for instance their Poincare' series is rational. It is an interesting problem to characterize classes of Koszul modules. Following the idea traced by Avramov, Iyengar and Sega, we take advantage of the existence of special filtration on $R$ for proving that large classes of $R$-modules over Koszul rings are Koszul modules. By using this tool we reprove and extend some results obtained by Fitzgerald.

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

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.

A genus explanation of the Buchsbaum-Rim multiplicity

We study the Buchsbaum-Rim multiplicity, ab inicio, through a Koszul-Čech spectral sequence. We show that the Buchsbaum-Rim multiplicity is the arithmetic genus (Euler characteristic) of Koszul homology sheaves on a projective space over the base scheme.