Locus of non-very stable bundles and its geometry

Let X be a smooth projective curve over complex numbers of arbitrary genus. In this paper we show that the locus of non-very stable bundles of rank 2 and determinant isomorphic to a fixed line bundle over X of degree 1 is a closed subvariety of codimension 1. We also give an explicit description of this closed subvariety for the genus 2 case.