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

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.