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arXiv · 1202.4948

Representing stable complexes on projective spaces

Jason Lo·Ziyu Zhang
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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.

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Jason Lo, Ziyu Zhang. 2012-02-22. Representing stable complexes on projective spaces. https://arxiv.org/abs/1202.4948

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