We relate the geometry of the resonance varieties
associated to a commutative differential graded algebra
model of a space to the finiteness properties of the
completions of its Alexander-type invariants. We also
describe in simple algebraic terms the non-translated
components of the degree-one characteristic
varieties for a class of non-proper complex manifolds.
Key Words: Resonance varieties, characteristic
varieties, Alexander invariants, completion, Gysin models, intersection form.
2000 Mathematics Subject Classification: Primary: 14M12, 55N25,
Secondary: 14F35, 20J05.
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