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

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.

13 pages, M2 codes in Appendix. Comments welcome!