$\mathbb{A}^1$-connectedness of moduli of vector bundles on a stacky curve

Source abstract

Let $\mathfrak{C}$ be a projective stacky curve over an infinite field, together with a generating sheaf $\mathcal{E}$. We consider the moduli stack of $\mathcal{E}$-semistable vector bundles of fixed determinant and multiplicities on $\mathfrak{C}$, and show that the moduli stack of such bundles is $\mathbb{A}^1$-connected. As a consequence, we conclude that the moduli stack of parabolic $α$-semistable vector bundles of fixed determinant and parabolic type on a connected smooth projective curve is $\mathbb{A}^1$-connected.