Cycles in the universal moduli stack of bundles of rank two over genus two curves

TL;DR

The paper conjectures the structure of the Chow ring of the universal moduli stack of rank two bundles over genus two hyperelliptic curves and proves it, providing explicit generators and relations.

Contribution

It introduces a conjecture for the Chow ring structure and proves it for rank two, genus two cases, with explicit generators and relations.

Findings

Chow ring is tautological for the studied case

Explicit generators and relations are obtained

Chow rings of products of universal Jacobians are computed

Abstract

We present a conjecture for the Chow ring of the universal moduli stack of bundles over hyperelliptic curves and prove it for rank and genus two. Consequently, we obtain explicit generators and relations to conclude that the Chow ring is tautological. In addition, we compute the Chow rings of products of universal Jacobians over genus two curves.