2016/11/12 by Amanda Croll, Croll, Amanda, Roger Dellaca +15
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1611.04001
Let k be a field and R a standard graded k-algebra. We denote by\n\HR the homology algebra of the Koszul complex on a minimal\nset of generators of the irrelevant ideal of R. We discuss the relationship\nbetween the multiplicative structure of \HR and the property\nthat R is a Koszul algebra. More generally, we work in the setting of local\nrings and we show that certain conditions on the multiplicative structure of\nKoszul homology imply strong homological properties, such as existence of\ncertain Golod homomorphisms, leading to explicit computations of Poincar 'e\nseries. As an application, we show that the Poincar 'e series of all finitely\ngenerated modules over a stretched Cohen-Macaulay local ring are rational,\nsharing a common denominator.\n