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, which extends the earlier result of Choe and Hwang (Math. Z. 253 (2006) 253–281, Main theorem).