The moduli space of semistable holomorphic vector bundles of fixed rank and fixed determinant line bundle on a compact Riemann surface is known to be compact itself. (In particular, when the rank is $1$, this space is just a single point, in the Picard group.)
When the rank is $2$ or more, is there a direct way to see that the moduli space is compact?
By "direct", I mean I'd like to be able to see this without appealing to flat connections, representations of the fundamental group, or Yang-Mills theory.