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The Borel-Serre Compactification for the Classifying Space of Hodge Structures

John Scherk
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Abstract

A 1-parameter variation of Hodge structures corresponds to a holomorphic, horizontal, locally liftable map into a classifying space of Hodge structures. In this paper it is shown that such a map has a limit in the reductive Borel-Serre compactification of the classifying space. The boundary component in which the limit lies is a union over possible polarizations of classifying spaces of Hodge structures on the primitive parts. It is discussed which boundary components can contain such limit points.

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BibTeXRIS

John Scherk. 2014-03-20. The Borel-Serre Compactification for the Classifying Space of Hodge Structures. https://arxiv.org/abs/math/0509319

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