$\mathbb{A}^1$--connectedness of moduli stack of semi-stable and parabolic semi-stable vector bundles over a curve

Sujoy Chakraborty; Sourav Holme Choudhury

Paper

$\mathbb{A}^1$--connectedness of moduli stack of semi-stable and parabolic semi-stable vector bundles over a curve

Abstract

Let

be an irreducible smooth projective curve of genus

over an algebraically closed field. We prove that the moduli stack of semi-stable vector bundles on

of fixed rank and determinant is

--connected. We also show that the moduli stack of quasi-parabolic vector bundles with a fixed determinant and a given quasi-parabolic data along a set of points in

, as well as its open substacks consisting of

-semistable vector bundles for any system of weights

, are also

-connected.