The pure cohomology of multiplicative quiver varieties

Kevin McGerty ^[1] ; Thomas Nevins ^[2]
1. [1] University of Oxford
  
  University of Oxford
  
  Oxford District, Reino Unido
2. [2] University of Illinois at Urbana-Champaign, USA
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 1, 2021
Idioma: inglés
DOI: 10.1007/s00029-020-00606-1
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Resumen
- To a quiver Q and choices of nonzero scalars qi, non-negative integers αi, and integers θi labeling each vertex i, Crawley-Boevey–Shaw associate a multiplicative quiver variety Mqθ(α), a trigonometric analogue of the Nakajima quiver variety associated to Q, α, and θ. We prove that the pure cohomology, in the Hodge-theoretic sense, of the stable locus Mqθ(α)s is generated as a Q-algebra by the tautological characteristic classes. In particular, the pure cohomology of genus g twisted character varieties of GLn is generated by tautological classes.