Moduli of parabolic sheaves and filtered Kronecker modules

We give the functorial moduli construction of pure parabolic sheaves in the sense of Álvarez-Cónsul and A. King by using the moduli of filtered Kronecker modules which we introduced in our earlier work. We also use a version of S. G. Langton’s result to deduce the projectivity of the moduli of pure parabolic sheaves of maximal dimension. As an application of functorial moduli construction, we can get the morphisms at the level of moduli stacks.