# Chow Group of 1-cycles of the Moduli of Parabolic Bundles Over a Curve

## TL;DR

This paper investigates the structure of the Chow group of 1-cycles on the moduli space of semistable parabolic vector bundles over a curve, showing invariance under weight variation and providing explicit descriptions in specific cases.

## Contribution

It demonstrates the invariance of the Chow group of 1-cycles under generic weight variation and explicitly describes this group for rank 2 bundles with fixed determinant.

## Key findings

- Chow group of 1-cycles is invariant under generic weight changes.
- Explicit description of the Chow group for rank 2 bundles with fixed determinant.
- Provides a concrete understanding of the cycle structure in the moduli space.

## Abstract

We study the Chow group of 1-cycles of the moduli space of semistable parabolic vector bundles of fixed rank, determinant and a generic weight over a nonsingular projective curve over $\mathbb{C}$ of genus at least 3. We show that, the Chow group of 1-cycles remains isomorphic as we vary the generic weight. As a consequence, we can give an explicit description of the Chow group in the case of rank 2 and determinant $\mathcal{O}(x)$, where $x\in X$ is a fixed point.