Topology of affine bow varieties and Zastavas

Abstract: Cherkis bow varieties were introduced as an ADHM type description of moduli spaces of U(n)-instantons on the Taub-NUT space equivariant under a cyclic group Z/mZ-action. An algebro-geometric description using quivers was constructed by Nakajima-Takayama, who have also shown that they generalise Na kajima quiver varieties, in particular Hilbert schemes of points on the affine plane. We compute the equivariant K-theory of their torus fixed points and give formulas for the generating series of their Euler numbers/motives. These series generalise the results of Ellingsrud-Stromme-G¨ottsche. As a special case, we obtain formulas for Drinfeld’s Zastavas. Joint work with Richárd Rimányi.