Cohomology jump loci of quasi-compact Kähler manifolds

2017/02/07 by Budur, Nero, Wang, Botong · 1 citation
#14B12 #53C55 #55N25 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.02186

Abstract

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.

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• The effective Chen ranks conjecture

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