Koszul algebras, introduced by Priddy, are positively graded K-algebras R whose residue fieldK has a linear free resolution as an R-module. In these lectures we deal with standard graded commutative K-algebras, that is, quotient rings of the polynomial ring S by homogeneous ideals. The program of the lectures is the following: Lecture 1: Koszul algebras and Castelnuovo–Mumford regularity. Lecture 2: Bounds for the degrees of the syzygies of Koszul algebras. Lecture 3: Veronese algebras and algebras associated with collections of hyperspaces.
Koszul Algebras and Their Syzygies
CONCA, ALDO
2014-01-01
Abstract
Koszul algebras, introduced by Priddy, are positively graded K-algebras R whose residue fieldK has a linear free resolution as an R-module. In these lectures we deal with standard graded commutative K-algebras, that is, quotient rings of the polynomial ring S by homogeneous ideals. The program of the lectures is the following: Lecture 1: Koszul algebras and Castelnuovo–Mumford regularity. Lecture 2: Bounds for the degrees of the syzygies of Koszul algebras. Lecture 3: Veronese algebras and algebras associated with collections of hyperspaces.
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