A construction of Chern classes of parabolic vector bundles

TL;DR

This paper develops a method to define Chern classes for parabolic vector bundles by constructing their projectivization and tautological line bundle, extending classical concepts to the parabolic setting.

Contribution

It introduces a novel construction of parabolic Chern classes using projectivization and tautological line bundles, generalizing classical vector bundle theory.

Findings

Constructed projectivization and tautological line bundle for parabolic vector bundles.

Provided a new method to define parabolic Chern classes.

Extended classical vector bundle concepts to the parabolic case.

Abstract

Given a parabolic vector bundle, we construct for it a projectivization and tautological line bundle. These are analogs of the projectivization and tautological line bundle for an usual vector bundle. Using these we give a construction of the parabolic Chern classes.