Pure and Applied Mathematics Quarterly
Volume 16 (2020)
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
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