Moduli stacks of stable toric quasimaps

Abstract

We construct new "virtually smooth" modular compactifications of spaces of maps from nonsingular curves to smooth projective toric varieties. They generalize Givental's compactifications, when the complex structure of the curve is allowed to vary and markings are included, and are the toric counterpart of the moduli spaces of stable quotients introduced by Marian, Oprea, and Pandharipande to compactify spaces of maps to Grassmannians. A brief discussion of the resulting invariants and their (conjectural) relation with Gromov-Witten theory is also included.

Published version

References in corpus (6)

• The intrinsic normal cone
• Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
• The moduli space of stable quotients
• Quantum D-modules and generalized mirror transformations
• Another way to enumerate rational curves with torus actions
• Genus-One Stable Maps, Local Equations, and Vakil-Zinger's desingularization

Cited by in corpus (39)

• The moduli space of stable quotients
• A Mathematical Theory of the Gauged Linear Sigma Model
• 13/2 ways of counting curves
• Mirror Theorem for Elliptic Quasimap Invariants
• Moduli of stable maps in genus one and logarithmic geometry I
• Higher genus quasimap wall-crossing for semi-positive targets
• Quasimap Wall-crossings and Mirror Symmetry
• Higher-genus wall-crossing in the gauged linear sigma model
• Virtual cycles of stable (quasi)-maps with fields
• A smooth compactification of the space of genus two curves in projective space via logarithmic geometry and Gorenstein curves
• The Abelian-Nonabelian Correspondence for $I$-functions
• Relative quasimaps and mirror formulae
• Quasimap wall-crossing for GIT quotients
• A Brief Survey of FJRW Theory
• Wall-crossing in genus zero quasimap theory and mirror maps
• Local B-model Yukawa couplings from A-twisted correlators
• A Fock Sheaf For Givental Quantization
• Virtual classes for the working mathematician
• Genus one GW invariants of quintic threefolds via MSP localization
• Orbifold Quasimap Theory
• Scattering amplitudes of stable curves
• Stable quotients and the holomorphic anomaly equation
• From equivariant volumes to equivariant periods
• Stable quasimaps to holomorphic symplectic quotients
• A new method toward the Landau-Ginzburg/Calabi-Yau correspondence via quasi-maps
• Quasimaps to moduli spaces of sheaves
• Stable maps and stable quotients
• A mirror theorem for Gromov-Witten theory without convexity
• On tau-functions for the KdV hierarchy
• Equivariant holomorphic anomaly equation
• Higher-genus wall-crossing in Landau-Ginzburg theory
• Quasimaps to GIT fiber bundles and applications
• The Moduli Space in the Gauged Linear Sigma Model
• Symplectic cuts and open/closed strings I
• The local/logarithmic correspondence and the degeneration formula for quasimaps
• Gromov-Witten invariants of Calabi-Yau fibrations
• $K$-theoretic quasimap wall-crossing
• A survey on mixed spin P-fields
• Vanishing of Gromov-Witten invariants of product of P1