Moduli spaces of slope-semistable pure sheaves.

We construct a moduli space of slope-semistable pure sheaves, generalizing a result given by Huybrechts and Lehn for torsion-free sheaves with fixed determinant on a smooth surface. An important feature of our construction is that we do not fix the determinant of sheaves. We also provide an effective restriction theorem for slope-stable pure sheaves following an approach due to Langer.