Higher resonance schemes and Koszul modules of simplicial complexes.

Each connected graded, graded-commutative algebra of finite type over a field of characteristic zero defines a complex of finitely generated, graded modules over a symmetric algebra, whose homology graded modules are called the of . In this note, we investigate the geometry of the support loci of these modules, called the of the algebra. When is the exterior Stanley-Reisner algebra associated to a finite simplicial complex , we show that the resonance schemes are reduced.