Resonance varieties and Dwyer–Fried invariants

The Dwyer–Fried invariants of a finite cell complex X are the subsets Ωr(X) of the Grassmannian of r-planes in H1(X,Q) which parametrize the regular Zr-covers of X having finite Betti numbers up to degree i. In previous work, we showed that each Ω-invariant is contained in the complement of a union of Schubert varieties associated to a certain subspace arrangement in H1(X,Q). Here, we identify a class of spaces for which this inclusion holds as equality. For such “straight” spaces X, all the data required to compute the Ω-invariants can be extracted from the resonance varieties associated to the cohomology ring H∗(X,Q). In general, though, translated components in the characteristic varieties affect the answer.