Two infinite series of moduli spaces of rank 2 sheaves on $\mathbb{P}^3$

Marcos Jardim; Dimitri Markushevich; Alexander S. Tikhomirov

doi:10.1007/s10231-016-0630-3

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arXiv · 1604.01605

Two infinite series of moduli spaces of rank 2 sheaves on $\mathbb{P}^3$

Marcos Jardim·Dimitri Markushevich·Alexander S. Tikhomirov

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Abstract

We describe new components of the Gieseker--Maruyama moduli scheme $\mathcal{M}(n)$ of semistable rank 2 sheaves $E$ on $\mathbb{P}^3$ with $c_1(E)=0$, $c_2(E)=n$ and $c_3(E)=0$ whose generic point corresponds to non locally free sheaves. We show that such components grow in number as $n$ grows, and discuss how they intersect the instanton component. As an application, we prove that $\mathcal{M}(2)$ is connected, and identify a connected subscheme of $\mathcal{M}(3)$ consisting of 7 irreducible components.

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Marcos Jardim, Dimitri Markushevich, Alexander S. Tikhomirov. 2016-04-06. Two infinite series of moduli spaces of rank 2 sheaves on $\mathbb{P}^3$. https://doi.org/10.1007/s10231-016-0630-3

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