An obstruction bundle relating Gromov-Witten invariants of curves and Kahler surfaces

2009/09/20 by Junho Lee, Lee, Junho, Thomas H. Parker +1
Mathematics · #14N35 #53D45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.0909.3610

openalex publication_date 2009/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [LP] the authors defined symplectic "Local Gromov-Witten invariants" associated to spin curves and showed that the GW invariants of a Kahler surface X with p_g>0 are a sum of such local GW invariants. This paper describes how the local GW invariants arise from an obstruction bundle (in the sense of Taubes) over the space of stable maps into curves. Together with the results of [LP], this reduces the calculation of the GW invariants of complex surfaces to computations in the GW theory of curves.

Citations

• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds

Related

• Sum Formulas for Local Gromov-Witten Invariants of Spin Curves
• Symplectic Gluing and Family Gromov-Witten Invariants
• A Structure Theorem for the Gromov-Witten Invariants of Kahler Surfaces
• Family Gromov-Witten Invariants for Kahler Surfaces
• Gromov--Witten invariants with naive tangency conditions