The Essential Dimension of Stacks of Parabolic Vector Bundles over Curves

We find upper bounds on the essential dimension of the moduli stack of parabolic vector bundles over a curve. When there is no parabolic structure, we improve the known upper bound on the essential dimension of the usual moduli stack. Our calculations also give lower bounds on the essential dimension of the semistable locus inside the moduli stack of vector bundles of rank $r$ and degree $d$ without parabolic structure.