2007/10/15 by Christian Schnell, Schnell, Christian
Mathematics · #14C30 #32S40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #msc:14C30 #msc:32S40
paper · pdf · doi:10.48550/arxiv.0710.2869
17 pages
openalex publication_date 2007/10/15 · arxiv created 2007/10/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A local system H on a complex manifold M can be viewed in two ways--either as a locally free sheaf, or as a union of covering spaces T = T(H). When M is an open set in a bigger manifold, the local system will generally not extend, because of local monodromy. This paper proposes an extension of the local system as an analytic space, in the case when the complement of M has normal crossing singularities, and the local system is unipotent along the boundary divisor. The analytic space is obtained by taking the closure of T inside the total space of Deligne's canonical extension of the associated vector bundle. It is not normal, but its normalization is locally toric.