Let $S$ be a $K3$ surface and $H$ an ample line bundle on it. Fix a Mukai vector $v\in H^\*(S,\mathbb Z)$. If $v$ is primitive, it turns out that Gieseker stability w.r.t.$H$ coincides with Gieseker semistability w.r.t. $H$. Does the same hold for $\mu\_H$-stability, too?



When do stability and semistability coincide?
If the rank and degree (wrt $H$) are coprime, then $\mu$-stability and $\mu$-semistability coincide. The argument is the same as for Gieseker-stability, but simpler.


