scholarly journals Lech's inequality, the Stückrad–Vogel conjecture, and uniform behavior of Koszul homology

2019 ◽  
Vol 347 ◽  
pp. 442-472 ◽  
Author(s):  
Patricia Klein ◽  
Linquan Ma ◽  
Pham Hung Quy ◽  
Ilya Smirnov ◽  
Yongwei Yao
Keyword(s):  
Koszul Homology

On the Koszul homology modules for the powers of a multiplicity system

Mathematika ◽  
1986 ◽  
Vol 33 (1) ◽  
pp. 96-101 ◽  
Author(s):  
J-L. García Roig ◽  
D. Kirby
Keyword(s):  
Koszul Homology

scholarly journals Estimates for Hilbertian Koszul homology

2008 ◽  
Vol 255 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Xiang Fang
Keyword(s):  
Koszul Homology

Koszul Homology of Cohen-Macaulay Rings with Linear Resolutions

1992 ◽  
Vol 115 (1) ◽  
pp. 51 ◽  
Author(s):  
Carlos Renteria ◽  
Rafael H. Villarreal
Keyword(s):  
Koszul Homology

scholarly journals DETECTING KOSZULNESS AND RELATED HOMOLOGICAL PROPERTIES FROM THE ALGEBRA STRUCTURE OF KOSZUL HOMOLOGY

2018 ◽  
Vol 238 ◽  
pp. 47-85 ◽  
Author(s):  
AMANDA CROLL ◽  
ROGER DELLACA ◽  
ANJAN GUPTA ◽  
JUSTIN HOFFMEIER ◽  
VIVEK MUKUNDAN ◽  
...  
Keyword(s):  
Poincaré Series ◽  
Koszul Complex ◽  
Local Rings ◽  
Common Denominator ◽  
Algebra Structure ◽  
Koszul Algebra ◽  
Multiplicative Structure ◽  
Poincare Series ◽  
Koszul Homology ◽  
Finitely Generated Modules

Let $k$ be a field and $R$ a standard graded $k$-algebra. We denote by $\operatorname{H}^{R}$ the homology algebra of the Koszul complex on a minimal set of generators of the irrelevant ideal of $R$. We discuss the relationship between the multiplicative structure of $\operatorname{H}^{R}$ and the property that $R$ is a Koszul algebra. More generally, we work in the setting of local rings and we show that certain conditions on the multiplicative structure of Koszul homology imply strong homological properties, such as existence of certain Golod homomorphisms, leading to explicit computations of Poincaré series. As an application, we show that the Poincaré series of all finitely generated modules over a stretched Cohen–Macaulay local ring are rational, sharing a common denominator.

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