The pure cohomology of multiplicative quiver varieties

2019/03/21 by Kevin McGerty, McGerty, Kevin, Thomas Nevins +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1903.08799

arxiv created 2019/03/21 · arxiv updated 2019/03/22

Abstract

To a quiver Q and choices of nonzero scalars q_i, non-negative integers α_i, and integers θ_i labeling each vertex i, Crawley-Boevey--Shaw associate a "multiplicative quiver variety" M_θ^q(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 M_θ^q(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 GL_n is generated by tautological classes.

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