2003/06/22 by Jim Bryan, Bryan, Jim, Rahul Pandharipande +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Geometry and complex manifolds #math.AG
paper · pdf · doi:10.48550/arxiv.math/0306316
Version to appear in Duke. Section 6 has been removed and incorporated into another paper
openalex publication_date 2003/06/22 · arxiv created 2004/05/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We continue our study of the local Gromov-Witten invariants of curves in Calabi-Yau 3-folds. We define relative invariants for the local theory which give rise to a 1+1-dimensional TQFT taking values in the ring Q[[t]]. The associated Frobenius algebra over Q[[t]] is semisimple. Consequently, we obtain a structure result for the local invariants. As an easy consequence of our structure formula, we recover the closed formulas for the local invariants in case either the target genus or the degree equals 1.