Moduli of parabolic sheaves and filtered Kronecker modules

We give functorial moduli construction of pure parabolic sheaves, in the sense of Alvarez-Consul and A. King, using the moduli of filtered Kronecker modules we introduced in our earlier work. We also use a version of S. G. Langton’s result due to K. Yokogawa to deduce the projectivity of 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.