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.

73 pages, major revision following the referee's suggestions, published version

References in corpus (19)

• The intrinsic normal cone
• Curve counting via stable pairs in the derived category
• Topological Reduction of 4D SYM to 2D $\sigma$--Models
• The moduli space of stable quotients
• Moduli stacks of stable toric quasimaps
• Wall-Crossings in Toric Gromov-Witten Theory I: Crepant Examples
• Holomorphic anomaly equations and the Igusa cusp form conjecture
• Coherent Tannaka duality and algebraicity of Hom-stacks
• Gromov-Witten invariants of the Hilbert schemes of points of a K3 surface
• Quasimap Wall-crossings and Mirror Symmetry
• Gromov-Witten theory of banded gerbes over schemes
• Moduli spaces of stable quotients and wall-crossing phenomena
• Virtual push-forwards
• Quasimap wall-crossing for GIT quotients
• Multiple cover formulas for K3 geometries, wall-crossing, and Quot schemes
• Quasimaps to moduli spaces of sheaves on a $K3$ surface
• Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface
• Gromov-Witten/Hurwitz wall-crossing
• Enumerative mirror symmetry for moduli spaces of Higgs bundles and S-duality

Cited by in corpus (1)

• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence