Local systems on analytic germ complements

Abstract

We prove that the cohomology jump loci of rank one local systems on the complement in a small ball of a germ of a complex analytic set are finite unions of torsion translates of subtori. This is a generalization of the classical Monodromy Theorem stating that the eigenvalues of the monodromy on the cohomology of the Milnor fiber of a germ of a holomorphic function are roots of unity.

v4: references adjusted. Final version

References in corpus (3)

• Recent results on cohomology jump loci
• Zeta functions and Alexander modules
• Cohomology jump loci of compact Kähler manifolds

Cited by in corpus (3)

• The monodromy theorem for compact Kähler manifolds and smooth quasi-projective varieties
• Spectral pairs, Alexander modules, and boundary manifolds
• Cohomology support loci of local systems