Algebraic models, Alexander-type invariants, and Green-Lazarsfeld sets

TL;DR

This paper explores the relationship between algebraic models of spaces, Alexander invariants, and resonance varieties, providing new insights into their geometric and algebraic properties.

Contribution

It establishes a connection between the geometry of resonance varieties and the finiteness of Alexander-type invariants, and describes characteristic varieties algebraically for certain complex manifolds.

Findings

Resonance varieties relate to the finiteness of Alexander invariants.

Non-translated components of characteristic varieties are described algebraically.

Provides a framework linking geometry and algebra in complex manifolds.

Abstract

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.