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

TL;DR

This paper computes equivariant K-theory and motivic invariants of affine type A bow varieties, deriving generating series formulas, exploring modularity, and relating them to known geometric and partition function results.

Contribution

It introduces refined motivic formulas for bow varieties, extending Nakajima quiver variety results, and defines a parabolic Nekrasov partition function with new relations.

Findings

Formulas for Euler number generating series of bow varieties

Modularity observed in certain cases

Relation between parabolic and classical Nekrasov partition functions

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.