Unirationality of the universal moduli space of semistable bundles over smooth curves

Shubham Saha

Published 2024-02-01, updated 2024-06-14Version 2

We construct explicit dominant, rational morphisms from projective bundles over rational varieties to relevant moduli spaces, showing their unirationality. These constructions work for $U_{r,d,g}$; for all ranks, degrees and genus $2\leq g \leq 9$. Furthermore, the arguments presented also show that a similar conclusion can be made for $U_{r, \mathcal{L}, g}$ for all $r,d$ and unirational $M_g$