resonance varieties
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2021 ◽  
Author(s):  
Alexander I. Suciu

Abstract We study the integral, rational, and modular Alexander invariants, as well as the cohomology jump loci of groups arising as extensions with trivial algebraic monodromy. Our focus is on extensions of the form 1→K→G→Q→1, where Q is an abelian group acting trivially on H1(K;ℤ), with suitable modifications in the rational and mod-p settings. We find a tight relationship between the Alexander invariants, the characteristic varieties, and the resonance varieties of the groups K and G. This leads to an inequality between the respective Chen ranks, which becomes an equality in degrees greater than 1 for split extensions.


2019 ◽  
Vol 150 (6) ◽  
pp. 3001-3027 ◽  
Author(s):  
Alexander I. Suciu

AbstractWe explore the constraints imposed by Poincaré duality on the resonance varieties of a graded algebra. For a three-dimensional Poincaré duality algebra A, we obtain a fairly precise geometric description of the resonance varieties ${\cal R}^i_k(A)$.


2019 ◽  
Vol 110 ◽  
pp. 197-234 ◽  
Author(s):  
Alexander I. Suciu ◽  
He Wang

2016 ◽  
Vol 369 (2) ◽  
pp. 1309-1343 ◽  
Author(s):  
Daniela Anca Măcinic ◽  
Ştefan Papadima ◽  
Clement Radu Popescu ◽  
Alexander I. Suciu

Author(s):  
Stefan Papadima ◽  
Alexander I. Suciu

AbstractWe explore a relationship between the classical representation theory of a complex, semisimple Lie algebra 𝔤 and the resonance varieties


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