Pure and Applied Mathematics Quarterly

Volume 16 (2020)

Number 4

Special Issue: In Honor of Prof. Gert-Martin Greuel’s 75th Birthday

Guest Editors: Igor Burban, Stanislaw Janeczko, Gerhard Pfister, Stephen S.T. Yau, and Huaiqing Zuo

Cohomology jump loci of quasi-compact Kähler manifolds

Pages: 981 – 999

DOI: https://dx.doi.org/10.4310/PAMQ.2020.v16.n4.a3


Nero Budur (KU Leuven, Belgium)

Botong Wang (University of Wisconsin, Madison, Wi., U.S.A.)


We give two applications of the exponential Ax–Lindemann Theorem to local systems. One application is to show that for a connected topological space, the existence of a finite model of the real homotopy type implies linearity of the cohomology jump loci around the trivial local system. Another application is the linearity of the cohomology jump loci of rank one local systems on quasi-compact Kähler manifolds.


cohomology jump locus, local system, Kähler manifold

2010 Mathematics Subject Classification

14F35, 14F45, 32C35, 32Q55, 55N25

The first-named author was sponsored by FWO, KU Leuven OT, and Methusalem grants.

Received 4 January 2019

Accepted 23 October 2019

Published 13 November 2020