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VOL. 62 | 2012 Resonance varieties and Dwyer–Fried invariants
Alexander I. Suciu

Editor(s) Hiroaki Terao, Sergey Yuzvinsky


The Dwyer–Fried invariants of a finite cell complex $X$ are the subsets $\Omega^i_r (X)$ of the Grassmannian of $r$-planes in $H^1 (X, \mathbb{Q})$ which parametrize the regular $\mathbb{Z}^r$-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 $H^1 (X, \mathbb{Q})$. 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 $H^{\ast} (X, \mathbb{Q})$. In general, though, translated components in the characteristic varieties affect the answer.


Published: 1 January 2012
First available in Project Euclid: 24 November 2018

zbMATH: 1273.14110
MathSciNet: MR2933803

Digital Object Identifier: 10.2969/aspm/06210359

Primary: 20J05 , 55N25
Secondary: 14F35 , 32S22 , 55R80 , 57M07

Keywords: characteristic variety , Dwyer–Fried set , Free abelian cover , hyperplane arrangement , Kähler manifold , resonance variety , special Schubert variety , tangent cone , toric complex

Rights: Copyright © 2012 Mathematical Society of Japan


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