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

Jaya Iyer (1) , Carlos Simpson (2)

1 IMSc - Institute of Mathematical Sciences [Chennai]
2 JAD - Laboratoire Jean Alexandre Dieudonné

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 $i\geq 0$. 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.

Mots clés: Connections; Chow groups; de Rham cohomology; parabolic bundles; Lefschetz pencils

Domaines: Géométrie algébrique [math.AG]

Jaya Iyer, Carlos Simpson. A relation between the parabolic Chern characters of the de Rham bundles. 2006. ⟨hal-00021918v2⟩