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Resonance varieties and Dwyer-Fried invariants

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în volumul unei conferinţe

Autori: A. I. Suciu

Editorial: Arrangements of Hyperplanes (Sapporo 2009), H. Terao and S. Yuzvinsky, Kinokuniya, Advanced Studies in Pure Mathematics, 62, p.359-398, 2012.


The Dwyer-Fried invariants of a finite cell complex X are the subsets Omega^i_r(X) of the Grassmannian of r-planes in H^1(X,Q) which parametrize the regular Z^r-covers of X having finite Betti numbers up to degree i. In previous work, we showed that each Omega-invariant is contained in the complement of a union of Schubert varieties associated to a certain subspace arrangement in H^1(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 Omega-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.

Cuvinte cheie: Free abelian cover, characteristic variety, resonance variety, tangent cone, Dwyer-Fried set, special Schubert variety, toric complex, Kaehler manifold, hyperplane arrangement