Representing stable complexes on projective spaces

We give an explicit proof of a Bogomolov-type inequality for c3c3 of reflexive sheaves on P3P3. Then, using resolutions of rank-two reflexive sheaves on P3P3, we prove that the closed points of some strata of the moduli of rank-two complexes that are both PT-stable and dual-PT-stable can be given by the structure of quotient stacks. Using monads, we apply the same techniques to P2P2 and obtain similar results for some strata of the moduli of Bridgeland-stable complexes.