Quasimaps to moduli spaces of sheaves

Abstract

We develop a theory of quasimaps to a moduli space of sheaves M on a surface S. Under some assumptions, we prove that moduli spaces of quasimaps are proper and carry a perfect obstruction theory. Moreover, they are naturally isomorphic to moduli spaces of sheaves on threefolds $S\times C$ , where C is a nodal curve. Using Zhou’s theory of entangled tails, we establish a wall-crossing formula which therefore relates the Gromov–Witten theory of M and the Donaldson–Thomas theory of $S\times C$ with relative insertions. We evaluate the wall-crossing formula for Hilbert schemes of points $S^{[n]}$ , if S is a del Pezzo surface.

Keywords

• 14N35