Refinement of Kool-Thomas Invariant via Equivariant K-theoretic invariants

We are defining a refinement of Kool-Thomas invariants via K-theoretic invariants proposed by Nekrasov and Okounkov. We introduce two K-theory class on the moduli space that contain the information of the incidence of a point with a curve supporting a stable pair (F,s). The evaluation at t=1 of the contribution of pairs supported on S to the K-theoretic invariants gives the Kool-Thomas invariants. Moreover, the generating function of this contribution contains the same information with the generating function given by the refined curve counting on complex surfaces defined by Göttsche and Shende