Fixed point counts and motivic invariants of bow varieties of affine type A

2024/09/05 by Ádám Gyenge, Richárd Rimányi, Gyenge, Ádám +1
Mathematics · Physics and Astronomy · #16G20 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Primary 14D20 #Secondary 14D21

paper · pdf · doi:10.48550/arxiv.2409.03859

openalex publication_date 2024/09/05 · openalex created_date 2024/10/21 · openalex updated_date 2026/07/28

Abstract

We compute the equivariant K-theory of torus fixed points of Cherkis bow varieties of affine type A. We deduce formulas for the generating series of the Euler numbers of these varieties and observe their modularity in certain cases. We also obtain refined formulas on the motivic level for a class of bow varieties strictly containing Nakajima quiver varieties. These series hence generalise results of Nakajima-Yoshioka. As a special case, we obtain formulas for certain Zastava spaces. We define a parabolic analogue of Nekrasov's partition function and find an equation relating it to the classical partition function.

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• Bow varieties as symplectic reductions of T^*(G/P)
• Cherkis bow varieties and Coulomb branches of quiver gauge theories of affine type A
• Computing torus-equivariant K-theory of singular varieties
• Quasimaps to zero-dimensional A_∞-quiver varieties