The Essential Dimension of Stacks of Parabolic Vector Bundles over Curves

TL;DR

This paper establishes new bounds on the essential dimension of moduli stacks of parabolic vector bundles over curves, improving existing bounds and providing insights into the complexity of these moduli spaces.

Contribution

It introduces improved upper bounds for the essential dimension of parabolic vector bundle stacks and offers lower bounds for the semistable locus in non-parabolic cases.

Findings

Upper bounds on essential dimension of parabolic vector bundle stacks.

Improved upper bounds for the non-parabolic moduli stack.

Lower bounds on the essential dimension of the semistable locus.

Abstract

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.