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The spectrum of torsion free sheaves on $\mathbb{P}^3$ and applications

Research paper by Charles Almeida

Indexed on: 31 Mar '19Published on: 11 Mar '19Published in: arXiv - Mathematics - Algebraic Geometry



Abstract

We study the spectrum of rank $2$ torsion free sheaves on $\mathbb{P}^3$ with aim of producing examples of distinct irreducible components of the moduli space with the same spetrcum answering the question presented by Rao for the case of torsion free sheaves. In order to do so, we provide a full description of the spectrum of the sheaves in the moduli space of semistable rank $2$ torsion free sheaves on $\mathbb{P}^3$ with Chern classes $(c_1, c_2,c_3)$ equals to $(-1,2,0)$ and $(0,3,0)$.