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Koszul Algebras and Their Syzygies

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Combinatorial Algebraic Geometry

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2108))

Abstract

A Koszul algebra R is a N-graded K-algebra whose residue field K has a linear free resolution as an R-module. We present various characterizations of Koszul algebras and strong versions of Koszulness. Recent results on bounds of the degrees of the syzygies of a Koszul algebra are discussed. Finally we discuss in details the Koszul property of Veronese algebras and of algebras associated with collections of hyperspaces.

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Acknowledgements

We thank Giulio Caviglia, Alessio D’Alì, Emanuela De Negri and Dang Hop Nguyen for their valuable comments and suggestions upon reading preliminary versions of the present notes and Christian Krattenthaler for suggesting the proof of formula (19).

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  1. Dipartimento di Matematica, Università degli Studi di Genova, Genova, Italy

    Aldo Conca

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Conca, A. (2014). Koszul Algebras and Their Syzygies. In: Combinatorial Algebraic Geometry. Lecture Notes in Mathematics(), vol 2108. Springer, Cham. https://doi.org/10.1007/978-3-319-04870-3_1

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