Localization in Gromov-Witten Theory and Orbifold Gromov-Witten Theory

Abstract

In this expository article, we explain how to use localization to compute Gromov-Witten invariants of smooth toric varieties and orbifold Gromov-Witten invariants of smooth toric Deligne-Mumford stacks.

65 pages

References in corpus (4)

• Equivariant Gromov-Witten theory of one dimensional stacks
• Open orbifold Gromov-Witten invariants of [C^3/Z_n]: localization and mirror symmetry
• On computations of Hurwitz-Hodge integrals
• Localization and Gluing of Orbifold Amplitudes: The Gromov-Witten Orbifold Vertex

Cited by in corpus (18)

• A Mirror Theorem for Toric Stacks
• A short overview of the "Topological recursion"
• On the Remodeling Conjecture for Toric Calabi-Yau 3-Orbifolds
• All Genus Open-Closed Mirror Symmetry for Affine Toric Calabi-Yau 3-Orbifolds
• Higher-genus wall-crossing in the gauged linear sigma model
• Generalized Mariño-Vafa Formula and Local Gromov-Witten Theory of Orbi-curves
• Towards a quantum Lefschetz hyperplane theorem in all genera
• Higher genus relative and orbifold Gromov-Witten invariants of curves
• A Mirror Theorem for the Mirror Quintic
• Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds
• Double ramification cycles on the moduli spaces of admissible covers
• Orbifold Gromov--Witten theory of weighted blowups
• A Formula of the One-leg Orbifold Gromov-Witten Vertex and Gromov-Witten Invariants of the Local $\cB\bZ_m$ Gerbe
• Hypertoric geometry and Gromov-Witten theory
• Cyclic Hodge Integrals and Loop Schur Functions
• Gromov-Witten invariants of ${\mathrm{Sym}}^d{\mathbb{P}}^r$
• Polynomiality of ${\mathbb{Z}}_2$ Hurwitz-Hodge Integrals
• Hurwitz-Hodge integral identities from the cut-and-join equation