Wall-crossing for framed quiver moduli

Abstract

We investigate the wall-crossing phenomena for moduli of framed quiver representations. As main motivating examples, we present framed quivers for the type A flag manifolds, Nakajima quiver varieties of type A, framed moduli of sheaves on the projective plane, the blow-up, and the (-2)-curve, and the type A affine Laumon spaces. In particular, we give the residue formula for the type A flag manifold as an example of wall-crossing formula. We roughly explain the way developed by Mochizuki, that is, the localization technique on the enhanced master spaces, in the setting of framed quiver. Specifically, we examine the wall-crossing formulas for integrals of Euler classes over the framed quiver moduli spaces.