2023/07/17 by Maxim Jeffs, Yuan Yao, Jeffs, Maxim +3 · 1 citation
Mathematics · #53D37 #57R58 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2307.08180
openalex publication_date 2023/07/17 · openalex created_date 2023/07/19 · openalex updated_date 2026/07/28
We show that for singular hypersurfaces, a version of their genus-zero Gromov-Witten theory may be described in terms of a direct limit of fixed point Floer cohomology groups, a construction which is more amenable to computation and easier to define than the technical foundations of the enumerative geometry of more general singular symplectic spaces. As an illustration, we give a direct proof of closed-string mirror symmetry for nodal curves of genus greater than or equal to 2, using calculations of (co)product structures on fixed point Floer homology of Dehn twists due to Yao-Zhao.