Representing stable complexes on projective spaces

TL;DR

This paper proves a Bogomolov-type inequality for reflexive sheaves on projective spaces and shows certain moduli spaces of stable complexes are quotient stacks, advancing the understanding of stability conditions and moduli in algebraic geometry.

Contribution

It provides explicit inequalities for reflexive sheaves and demonstrates that specific moduli of stable complexes are quotient stacks, using resolutions and monads.

Findings

Established a Bogomolov-type inequality for $c_3$ of reflexive sheaves on $P^3$

Proved some strata of moduli of rank-two complexes are quotient stacks

Extended techniques to $P^2$ for Bridgeland-stable complexes

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.