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

By J. Iyer, Carlos Simpson. 2006

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In this paper, we consider the weight i de Rham–Gauss–Manin bundles on a smooth variety arising from a smooth projective morphism $${f:X_U\longrightarrow U}$$ 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d5946106e93fbd63e283c510f6c6cfe1cecb9cca

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Parabolic sheaves on logarithmic schemes (2010, background): “d Seshadri (see [MS80] and [Ses82]), and subsequently generalized to higher dimension by Maruyama and Yokogawa ([MY92]); this latter deﬁnition was later improved by Mochizuki ([Moc06]), Iyer–Simpson ([IS07]) and the ﬁrst author ([Bor09]). Another important insight is due to Biswas, who connected rat”
Katz's middle convolution algorithm (2006, methodology): “for every point qi the parabolic type is a divisor concentrated over roots of unity in S1, then as discussed in [19] [27] [108] [77], the parabolic bundle may also be viewed as a bundle on a Deligne-Mumford stack Z[ Q m ] obtained by assigning an integer m to the points qi.”
Local Systems on Proper Algebraic V -manifolds (2010, methodology): “has been used and studied by many authors, see for example Boden [18], Balaji et al [5], Biswas [11], Borne [20] [21] as well as [53] and [54].”
Kobayashi-Hitchin correspondence for tame harmonic bundles II (2006, background): “Proposition 2.54 (Simpson [18]) Let X be a smooth irreducible projective curve, and D be a simple divisor of X .”