# Singular loci of instanton sheaves on projective space

@article{Gargate2016SingularLO, title={Singular loci of instanton sheaves on projective space}, author={Michael Santos Gonzales Gargate and Marcos Jardim}, journal={International Journal of Mathematics}, year={2016}, volume={27}, pages={1640006} }

We prove that the singular locus of a rank 2 non-locally free instanton sheaf E on ℙ3 has pure dimension 1. Moreover, we also show that the dual and double dual of E are isomorphic locally free instanton sheaves, and that the sheaves ℰxt1(E,𝒪 ℙ3) and E∨∨/E are rank 0 instantons. We also provide explicit examples of instanton sheaves of ranks 3 and 4 illustrating that all of these claims are false for higher rank instanton sheaves.

#### 7 Citations

Compactification of the moduli space of minimal instantons on the Fano threefold $$V_4$$

- Mathematics
- European Journal of Mathematics
- 2021

We study semistable sheaves of rank 2 with Chern classes c1 = 0, c2 = 2 and c3 = 0 on the Fano threefold V4 of Picard number 1, degree 4 and index 2. We show that the moduli space of such sheaves is… Expand

Instanton sheaves and representations of quivers

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- Proceedings of the Edinburgh Mathematical Society
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Abstract We study the moduli space of rank 2 instanton sheaves on ℙ3 in terms of representations of a quiver consisting of three vertices and four arrows between two pairs of vertices. Aiming at an… Expand

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- 2019

The main goal of this thesis is the caracterization of rank 3 nstanton bundles in the complex projective space of dimension 3 without global sections. The used tool is the Hartshorne-Serre… Expand

The geometry of the moduli space of torsion free sheaves on projective spaces : Geometria dos espaços de moduli de feixes sem torção em espaços projetivos

- Physics
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Our goal is to study the geometry of moduli spaces of rank 2 sheaves on projective spaces. We present a new family of monads whose cohomology is a stable rank two vector bundle on P3. We also study… Expand

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- Mathematics
- 2017

We study the irreducible components of the moduli space of instanton sheaves on $\mathbb{P}^3$, that is rank 2 torsion free sheaves $E$ with $c_1(E)=c_3(E)=0$ satisfying $h^1(E(-2))=h^2(E(-2))=0$. In… Expand

New divisors in the boundary of the instanton moduli space

- Mathematics
- 2015

Let ${\mathcal I}(n)$ denote the moduli space of rank $2$ instanton bundles of charge $n$ on ${\mathbb P}^3$. We know from several authors that ${\mathcal I}(n)$ is an irreducible, nonsingular and… Expand

On the fixed locus of framed instanton sheaves
on ℙ3

- Mathematics
- 2018

Let $\mathbb{T}$ be the three dimensional torus acting on $\mathbb{P}^{3}$ and $\mathcal{M}^{\mathbb{T}}_{\mathbb{P}^{3}}(c)$ be the fixed locus of the corresponding action on the moduli space of… Expand

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