A relation between the parabolic Chern characters of the de Rham bundles

2006/03/29 by Jaya Nn Iyer, Iyer, Jaya N., Carlos Simpson +1 · 2 citations
Mathematics · #14C25 #14D05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0603677

openalex publication_date 2006/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the weight i de Rham--Gauss--Manin bundles on a smooth variety arising from a smooth projective morphism f:X_U\lrar U for i≥ 0. We associate to each weight i de Rham bundle, a certain parabolic bundle on S and consider their parabolic Chern characters in the rational Chow groups, for a good compactification S of U. We show the triviality of the alternating sum of these parabolic bundles in the (positive degree) rational Chow groups. This removes the hypothesis of semistable reduction in the original result of this kind due to Esnault and Viehweg.

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• Hyperbolicity and fundamental groups of complex quasi-projective varieties (II): via non-abelian Hodge theories
• Uniformization as Tannakian Reconstruction

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