  Each connected graded, graded-commutative algebra $A$ of finite type over a
field $\Bbbk$ of characteristic zero defines a complex of finitely generated,
graded modules over a symmetric algebra, whose homology graded modules are
called the (higher) Koszul modules of $A$. In this note, we investigate the
geometry of the support loci of these modules, called the resonance schemes of
the algebra. When $A=\Bbbk\langle \Delta \rangle$ is the exterior
Stanley-Reisner algebra associated to a finite simplicial complex $\Delta$, we
show that the resonance schemes are reduced. We also compute the Hilbert series
of the Koszul modules and give bounds on the regularity and projective
dimension of these graded modules. This leads to a relationship between
resonance and Hilbert series that generalizes a known formula for the Chen
ranks of a right-angled Artin group.
