Equivariant Gromov-Witten theory of one dimensional stacks

2009/03/05 by Paul D. Johnson, Johnson, Paul D. · 3 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0903.1068

openalex publication_date 2009/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In math.AG/0207233, Okounkov and Pandharipande gave an operator formalism for computing the equivariant Gromov-Witten theory of the projective line. This thesis extends their result to orbifold lines. In the effective case the theory is again governed by the 2-Toda hierarchy. In the ineffective case the decomposition conjecture of hep-th/0606034 is verified.

Citations

• On Gromov-Witten theory of root gerbes
• Gerby Localization, Z₃-Hodge Integrals and the GW Theory of C³/Z₃
• Gromov-Witten theory of orbicurves, the space of tri-polynomials and Symplectic Field Theory of Seifert fibrations

Cited by

• Localization and Gluing of Orbifold Amplitudes: The Gromov-Witten\n Orbifold Vertex
• Relations on Mbar_g,n via orbifold stable maps
• Quantum curve and bilinear Fermionic form for the orbifold Gromov-Witten theory of ℙ[r]

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• On Frobenius Manifolds from Gromov--Witten Theory of Orbifold Projective Lines with r orbifold points