Moduli Space of Sheaves and Categorified Commutator of Functors

Abstract

We construct a weak categorification of the quantum toroidal algebra action on the Grothendieck group of moduli space of stable (or framed) sheaves over an algebraic surface, which is constructed by Schiffmann-Vasserot and Neguţ. The new ingredient is two intersection-theoretic descriptions of the quadruple moduli space of stable sheaves.