The Chern Invariants for Parabolic Bundles at Multiple Points

TL;DR

This paper studies how parabolic Chern classes can be extended and classified for bundles on surfaces with multiple points, providing insights into their invariants at singularities.

Contribution

It introduces methods to analyze and classify possible parabolic Chern classes for bundles extended over resolutions of singularities at multiple points.

Findings

Classification of possible parabolic Chern classes

Extension methods for bundles over singularities

Insights into invariants at multiple points

Abstract

If $ D \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.