quiver bundles
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2020 ◽  
Vol 546 ◽  
pp. 432-456
Author(s):  
Claudio Bartocci ◽  
Ugo Bruzzo ◽  
Claudio L.S. Rava
Keyword(s):  

2020 ◽  
Vol 156 (4) ◽  
pp. 744-769
Author(s):  
Sergey Mozgovoy ◽  
Olivier Schiffmann

We prove a closed formula counting semistable twisted (or meromorphic) Higgs bundles of fixed rank and degree over a smooth projective curve of genus $g$ defined over a finite field, when the twisting line bundle degree is at least $2g-2$ (this includes the case of usual Higgs bundles). This yields a closed expression for the Donaldson–Thomas invariants of the moduli spaces of twisted Higgs bundles. We similarly deal with twisted quiver sheaves of type $A$ (finite or affine), obtaining in particular a Harder–Narasimhan-type formula counting semistable $U(p,q)$-Higgs bundles over a smooth projective curve defined over a finite field.


2019 ◽  
Vol 30 (03) ◽  
pp. 1850085
Author(s):  
Artur de Araujo

We review the theory of quiver bundles over a Kähler manifold, and then introduce the concept of generalized quiver bundles for an arbitrary reductive group [Formula: see text]. We first study the case when [Formula: see text] or [Formula: see text], interpreting them as orthogonal (respectively symplectic) bundle representations of the symmetric quivers introduced by Derksen–Weyman. We also study supermixed quivers, which simultaneously involve both orthogonal and symplectic symmetries. In particular, we completely characterize the polystable forms of such representations. Finally, we discuss Hitchin–Kobayashi correspondences for these objects.


2018 ◽  
Vol 199 (1) ◽  
pp. 137-146 ◽  
Author(s):  
P. B. Gothen ◽  
A. Nozad
Keyword(s):  

2017 ◽  
Vol 118 ◽  
pp. 51-66 ◽  
Author(s):  
Indranil Biswas ◽  
Georg Schumacher

2013 ◽  
Vol 24 (05) ◽  
pp. 1350038 ◽  
Author(s):  
BUMSIG KIM ◽  
HWAYOUNG LEE

Given a double quiver, we study homological algebra of twisted quiver sheaves with the moment map relation using the short exact sequence of Crawley-Boevey, Holland, Gothen, and King. Then in a certain one-parameter space of the stability conditions, we obtain a wall-crossing formula for the generalized Donaldson–Thomas invariants of the abelian category of framed twisted quiver sheaves on a smooth projective curve. To do so, we closely follow the approach of Chuang, Diaconescu and Pan in the ADHM quiver case, which makes use of the theory of Joyce and Song. The invariants virtually count framed twisted quiver sheaves with the moment map relation and directly generalize the ADHM invariants of Diaconescu.


2008 ◽  
Vol 139 (1) ◽  
pp. 99-120 ◽  
Author(s):  
Luis Álvarez-Cónsul
Keyword(s):  

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