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

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 $\alpha$-semistable vector bundles of fixed determinant and parabolic type on a connected smooth projective curve is ${\mathbb{A}}^1$-connected.

16 pages. Comments are welcome