Abstract EN:

In this thesis 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. The second part of the thesis we take D subset in X is a curve with multiple points in a surface, a parabolic bundle defined on (X, D) away from the singularities can be extended in several ways to a parabolic bundle on a resolution of singularities. We investigate the possible parabolic Chern classes for these extensions.