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

2005/09/14 by John Scherk, Scherk, John
Mathematics · #14D07 #32S35 #54D35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0509319

openalex publication_date 2005/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related

• Baily--Borel compactifications of period images and the b-semiampleness conjecture
• Limits of Hodge structures with quasi-unipotent monodromies
• Extension of Hodge norms at infinity
• Categories of complex variations of Hodge structure over compact K"ahler manifolds
• Variations of Hodge structure and orbits in flag varieties