%0 Journal Article %T Representing stable complexes on projective spaces %A Jason Lo %A Ziyu Zhang %J Mathematics %D 2012 %I arXiv %X We give an explicit proof of a Bogomolov-type inequality for $c_3$ of reflexive sheaves on $\mathbb{P}^3$. Then, using resolutions of rank-two reflexive sheaves on $\mathbb{P}^3$, we prove that some strata of the moduli of rank-two complexes that are both PT-stable and dual-PT-stable are quotient stacks. Using monads, we apply the same techniques to $\mathbb{P}^2$ and show that some strata of the moduli of Bridgeland-stable complexes are quotient stacks. %U http://arxiv.org/abs/1202.4948v2