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# 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

#### 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