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. 
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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
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
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
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
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 ${\mathbb P}_3$
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.
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
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