Upper bounds for the essential dimension of the moduli stack of ${\sl_{n}}$-bundles over a curve

TL;DR

This paper establishes upper bounds for the essential dimension of moduli stacks of SL_n-bundles over a curve, precisely computing it for prime power n and revealing cases where it differs from the stack's dimension.

Contribution

It provides new upper bounds for the essential dimension of SL_n-bundle moduli stacks and exact calculations when n is a prime power, highlighting differences from the dimension.

Findings

Exact essential dimension for prime power n

Upper bounds for non-prime power n

Essential dimension differs from the stack's dimension in some cases

Abstract

We find upper bounds for the essential dimension of various moduli stacks of $\sln$-bundles over a curve. When $n$ is a prime power, our calculation computes the essential dimension of the stack of stable bundles exactly and the essential dimension is not equal to the dimension in this case.