Representations of quivers on abelian categories and monads on projective varieties

Jardim, Marcos; Prata, Daniela Moura

doi:10.11606/issn.2316-9028.v4i3p399-423

Cited by 3 publications

(3 citation statements)

References 19 publications

(11 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

Section: Equivalence Between Categories Of Monads and Representationssupporting

confidence: 84%

Instanton sheaves and representations of quivers

Jardim,

da Silva

2019

Preprint

Self Cite

View full text Add to dashboard Cite

We study the moduli space of rank 2 instanton sheaves on P 3 in terms of representations of a quiver consisting of 3 vertices and 4 arrows between two pairs of vertices. Aiming at an alternative compactification for the moduli space of instanton sheaves, we show that for each rank 2 instanton sheaf, there is a stability parameter θ for which the corresponding quiver representation is θ-stable (in the sense of King), and that the space of stability parameters has a non trivial wall-and-chamber decomposition. Looking more closely at instantons of low charge, we prove that there are stability parameters with respect to which every representation corresponding to a rank 2 instanton sheaf of charge 2 is stable, and provide a complete description of the wall-and-chamber decomposition for representation corresponding to a rank 2 instanton sheaf of charge 1.

show abstract

Section: Equivalence Between Categories Of Monads and Representationssupporting

confidence: 84%

Instanton sheaves and representations of quivers

Jardim,

da Silva

2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…We construct an equivalence functor F between C and Q which restricts to the desired equivalences between their subcategories. Similar partial results in this direction were obtained in [8,9]. First, fix homogeneous coordinates [x 0 : x 1 : x 2 : x 3 ] of P 3 , and let {x 0 , x 1 , x 2 , x 3 } be the corresponding basis of H 0 (O P 3 (1)); one has a natural isomorphism…”

Section: Proposition 6 There Is An Equivalence Of Categories Betweensupporting

confidence: 60%

Instanton sheaves and representations of quivers

Jardim

Silva²

2020

Proceedings of the Edinburgh Mathematical Society

View full text Add to dashboard Cite

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 alternative compactification for the moduli space of instanton sheaves, we show that for each rank 2 instanton sheaf, there is a stability parameter θ for which the corresponding quiver representation is θ-stable (in the sense of King), and that the space of stability parameters has a non-trivial wall-and-chamber decomposition. Looking more closely at instantons of low charge, we prove that there are stability parameters with respect to which every representation corresponding to a rank 2 instanton sheaf of charge 2 is stable and provide a complete description of the wall-and-chamber decomposition for representation corresponding to a rank 2 instanton sheaf of charge 1.

show abstract

“…A functor X ∈ G(H) associates an object X (i) ∈ H to each node i ∈ G and a morphism X (ψ) ∈ Hom H X (i), X (j)(7.4) to each arrow i ψ − → j of G. G(H) is a linear Abelian category of global dimension at most 2, and all auto-equivalence σ of H induce an auto-equivalence 1 ⊗ σ of G(H)[79] …”

mentioning

confidence: 99%

Homological $S$-duality in 4d $\mathcal{N}=2$ QFTs

Caorsi

Cecotti

2018

Advances in Theoretical and Mathematical Physics

View full text Add to dashboard Cite

The S-duality group S(F ) of a 4d N = 2 supersymmetric theory F is identified with the group of triangle equivalences of its cluster category C (F ) modulo the subgroup acting trivially on the physical quantities. S(F ) is a discrete group commensurable to a subgroup of the Siegel modular group Sp(2g, Z) (g being the dimension of the Coulomb branch). This identification reduces the determination of the S-duality group of a given N = 2 theory to a problem in homological algebra. In this paper we describe the techniques which make the computation straightforward for a large class of N = 2 QFTs. The group S(F ) is naturally presented as a generalized braid group.The S-duality groups are often larger than expected. In some models the enhancement of S-duality is quite spectacular. For instance, a QFT with a huge S-duality group is the Lagrangian SCFT with gauge group SO(8) × SO(5) 3 × SO(3) 6 and half-hypermultiplets in the bi-and tri-spinor representations.

show abstract

Representations of quivers on abelian categories and monads on projective varieties

Cited by 3 publications

References 19 publications

Instanton sheaves and representations of quivers

Instanton sheaves and representations of quivers

Instanton sheaves and representations of quivers

Homological $S$-duality in 4d $\mathcal{N}=2$ QFTs

Contact Info

Product

Resources

About