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}
}
• Published 3 July 2014
• Mathematics
• International Journal of Mathematics
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.
8 Citations
Compactification of the moduli space of minimal instantons on the Fano threefold $$V_4$$
• Xuqiang Qin
• 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 isExpand
Instanton sheaves and representations of quivers
• Mathematics
• Proceedings of the Edinburgh Mathematical Society
• 2020
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 anExpand
Some results for rank 3 vector bundles, reflexive sheaves and instanton bundles in the complex projective space of dimension 3 : Alguns resultados sobre fibrados, feixes reflexivos e fibrados instanton de posto 3 no espaço projetivo complexo de dimensão 3
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-SerreExpand
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
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 studyExpand
Moduli spaces of rank 2 instanton sheaves on the projective space
• 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 $h^1(E(-2))=h^2(E(-2))=0$. InExpand
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 andExpand
On the fixed locus of framed instanton sheaves on ℙ3
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 ofExpand
Vertical asymptotics for Bridgeland stability conditions on 3-folds
Let X be a smooth projective threefold of Picard number one for which the generalized Bogomlov-Gieseker inequality holds. We characterize the limit Bridgeland semistable objects at large volume inExpand

References

SHOWING 1-10 OF 22 REFERENCES
Instanton sheaves on complex projective spaces
We study a class of torsion-free sheaves on complex projective spaces which generalize the much studied mathematical instanton bundles. Instanton sheaves can be obtained as cohomologies of linearExpand
ADHM CONSTRUCTION OF PERVERSE INSTANTON SHEAVES
• Mathematics
• Glasgow Mathematical Journal
• 2014
Abstract We present a construction of framed torsion free instanton sheaves on a projective variety containing a fixed line which further generalises the one on projective spaces. This is done byExpand
Nondegenerate multidimensional matrices and instanton bundles
• Mathematics
• 2001
In this paper we prove that the moduli space of rank 2n symplectic instanton bundles on P 2n+1 , defined from the well-known monad condition, is affine. This result was not known even in the case n =Expand
Monads on projective spaces
• Mathematics
• 2003
Abstract.Let ℰ be a vector bundle on Pn. There is a strong relationship between ℰ and its intermediate cohomology modules. In the case where ℰ has low rank, we exploit this relationship to provideExpand
MODULI SPACES OF FRAMED PERVERSE INSTANTONS ON ℙ3
• Mathematics, Physics
• Glasgow Mathematical Journal
• 2010
Abstract We study moduli spaces of framed perverse instantons on ℙ3. As an open subset, it contains the (set-theoretical) moduli space of framed instantons studied by I. Frenkel and M. Jardim in [9].Expand
Monads on projective spaces
We classify for which a,b,c, and k there exists complexes with α injective and β surjective. Furthermore we show that when it exists, we may assume that α degenerates in P k in expected codimension,Expand
Irreducibility and Smoothness of the moduli space of mathematical 5--instantons over ${\mathbb P}_3$
• Mathematics
• 2002
We prove that the space of mathematical instantons with second Chern class 5 over ${\mathbb P}_3$ is smooth and irreducible. Unified and simple proofs for the same statements in case of second ChernExpand
Dedicated to the memory of Andrei Nikolaevich Tyurin MODULI OF MATHEMATICAL INSTANTON VECTOR BUNDLES WITH ODD c2 ON PROJECTIVE SPACE
Denote by In the set of isomorphism classes of n-instantons. This space is nonempty for any n ≥ 1 see, e.g., [BT], [NT]. The condition h(E) = 0 for a n-instanton E implies that E is stable in theExpand
Compactification of $M_{{\bf P}_3}(0,2)$ and Poncelet pairs of conics.
• Mathematics
• 1990
Let M(0, 2) denote the quasi-projective variety of isomorphism classes of stable rank 2 vector bundles on P 3 (C) with C 1 =0 and C 2 =2 . In this paper we study a natural (irreducible)Expand
Yang-Mills fields on quaternionic spaces
A study is made of solutions of the Yang-Mills equations over a quaternionic Kahler manifold. The corresponding notion of self-duality is interpreted in terms of holomorphic geometry on a twistorExpand