Naturality properties and comparison results for topological and infinitesimal embedded jump loci

摘要

We use augmented commutative differential graded algebra (ACDGA) models to study G-representation varieties of fundamental groups pi = pi(1 )(M) and their embedded cohomology jump loci, around the trivial representation 1. When the space M admits a finite family of maps, uniformly modeled by ACDGA morphisms, and certain finiteness and connectivity assumptions are satisfied, the germs at 1 of Hom(pi, G) and of the embedded jump loci can be described in terms of their infinitesimal counterparts, naturally with respect to the given families. This approach leads to fairly explicit answers when M is either a compact Kahler manifold, the complement of a central complex hyperplane arrangement, or the total space of a principal bundle with formal base space, provided the Lie algebra of the linear algebraic group G is a non-abelian subalgebra of sl(2) (C). (C) 2019 Elsevier Inc. All rights reserved.