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Abstract: A local system H on a complex manifold M can be viewed in two ways-either asa locally free sheaf, or as a union of covering spaces T = TH. When M is anopen set in a bigger manifold, the local system will generally not extend,because of local monodromy. This paper proposes an extension of the localsystem as an analytic space, in the case when the complement of M has normalcrossing singularities, and the local system is unipotent along the boundarydivisor. The analytic space is obtained by taking the closure of T inside thetotal space of Deligne-s canonical extension of the associated vector bundle.It is not normal, but its normalization is locally toric.

Author: Christian Schnell


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