Local systems on analytic germ complements

Nero Budur; Botong Wang

Local systems on analytic germ complements

Algebraic Geometry 2016-11-04 v4 Algebraic Topology Complex Variables

Authors: Nero Budur , Botong Wang

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.

Keywords

local-global principles cohomology theory

Cite

@article{arxiv.1508.07867,
  title  = {Local systems on analytic germ complements},
  author = {Nero Budur and Botong Wang},
  journal= {arXiv preprint arXiv:1508.07867},
  year   = {2016}
}