Homology, Homotopy and Applications

Volume 4 (2002)

Number 2

The Roos Festschrift volume

Koszul homology and Lie algebras with application to generic forms and points

Pages: 227 – 258

DOI: http://dx.doi.org/10.4310/HHA.2002.v4.n2.a11

Authors

R. Fröberg (Department of Mathematics, Stockholm University, Sweden)

C. Löfwal (Department of Mathematics, Stockholm University, Sweden)

Abstract

We study the Koszul dual for general superalgebras, and apply it to the Koszul homology of a graded algebra. We show that a part of the Koszul homology algebra is related to the homotopy Lie algebra by means of Koszul duality. This is used to study the ”Minimal Resolution Conjecture” and the ”Ideal Generating Conjecture” for sets of generic points in projective space, and for quotients of the polynomial ring (or exterior algebra) modulo generic quadratic forms.

Keywords

Koszul homology, Lie algebra, generic points, generic forms

2010 Mathematics Subject Classification

13D07, 14Mxx, 16E45

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