Representing stable complexes on projective spaces

Abstract

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.

27 pages

References in corpus (4)

• Construction of Hilbert and Quot Schemes
• Moduli of PT-Semistable Objects I
• Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces
• Linear and Steiner bundles on projective varieties