Abstract:This talk is based on the preprint
(https://arxiv.org/abs/2302.09245 ) by Dario Weissmann and Xucheng Zhang.
It also fits in the framework of the series of papers being written at
recent times by mathematicians like Jarod Alper, Jochen Heinloth etc with
the idea to rewrite the available literature about moduli spaces in the
language of stacks and avoiding GIT. The existence of the course moduli
space of semistable vector bundles on a smooth projective curve is a well
known result and the classical proof relies on the notion of semi-stable
points in GIT. This paper will try to give a stacky criteria to identify
the semi-stable sublocus of the stack of vector bundles. One of the main
contributions of this paper is to identify when the good/adequate moduli
space (as introduced by Alper, which is apriori an algebraic space)
becomes a scheme.