Calculating the parabolic Chern character of a locally abelian parabolic bundle

TL;DR

This paper derives explicit formulas for the parabolic Chern character of locally abelian parabolic bundles on smooth divisors, confirming consistency with previous results by Borne and Mochizuki.

Contribution

It provides explicit calculations of the parabolic Chern character for such bundles using Deligne-Mumford stacks, extending prior theoretical work.

Findings

Explicit formulas for ch_1, ch_2, and ch_3 are obtained.

The formulas agree with those previously established by Borne and Mochizuki.

The approach uses the stack-theoretic definition of parabolic bundles.

Abstract

We calculate the parabolic Chern character of a bundle with locally abelian parabolic structure on a smooth strict normal crossings divisor, using the definition in terms of Deligne-Mumford stacks. We obtain explicit formulas for $ch_1$, $ch_2$ and $ch_3$, and verify that these correspond to the formulas given by Borne for $ch_1$ and Mochizuki for $ch_2$.