Semistable rank 2 sheaves with singularities of mixed dimension on P3

Ivanov, Alexey N.; Tichomirov, Aleksandr S.‏

doi:10.1016/j.geomphys.2018.02.018

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Semistable rank 2 sheaves with singularities of mixed dimension on P³

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Tichomirov, Aleksandr S.‏
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.geomphys.2018.02.018
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Citation

Ivanov, A. N., & Tichomirov, A. S. (2018). Semistable rank 2 sheaves with singularities of mixed dimension on P³. Journal of Geometry and Physics, 129, 90-98. doi:10.1016/j.geomphys.2018.02.018.

Cite as: https://hdl.handle.net/21.11116/0000-0003-FC29-4

Abstract

We describe new irreducible components of the Gieseker-Maruyama moduli scheme
$\mathcal{M}(3)$ of semistable rank 2 coherent sheaves with Chern classes
$c_1=0,\ c_2=3,\ c_3=0$ on $\mathbb{P}^3$, general points of which correspond to sheaves whose singular loci contain components of dimensions both 0 and 1. These sheaves are produced by elementary transformations of stable reflexive rank 2 sheaves with $c_1=0,\ c_2=2,\ c_3=2$ or 4 along a disjoint union of a projective line and a collection of points in $\mathbb{P}^3$. The constructed
families of sheaves provide first examples of irreducible components of the Gieseker-Maruyama moduli scheme such that their general sheaves have singularities of mixed dimension.