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arXiv · 1302.4075

Jump loci in the equivariant spectral sequence

Stefan Papadima·Alexander I. Suciu
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Abstract

We study the homology jump loci of a chain complex over an affine \k-algebra. When the chain complex is the first page of the equivariant spectral sequence associated to a regular abelian cover of a finite-type CW-complex, we relate those jump loci to the resonance varieties associated to the cohomology ring of the space. As an application, we show that vanishing resonance implies a certain finiteness property for the completed Alexander invariants of the space. We also show that vanishing resonance is a Zariski open condition, on a natural parameter space for connected, finite-dimensional commutative graded algebras.

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BibTeXRIS

Stefan Papadima, Alexander I. Suciu. 2013-02-17. Jump loci in the equivariant spectral sequence. https://doi.org/10.4310/mrl.2014.v21.n4.a13

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