Rational Chow ring of the universal moduli space of semistable rank two bundles over genus two curves

Abstract

We determine the rational Chow ring of the universal moduli space of rank $2$ semistable bundles over smooth curves of genus $2$, and show that it is generated by certain tautological classes. In the process, we obtain Chow rings of universal Jacobians over genus $2$ curves with marked Weierstrass points, and the Chow ring of the universal pointed Jacobian. This further provides alternate computations to arxiv:2404.12607 in the genus $2$ case.