2018/09/11 by Tom Coates, Coates, Tom, Cristina Manolache +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG
paper · pdf · doi:10.48550/arxiv.1809.04162
38 pages
arxiv created 2018/09/11 · openalex publication_date 2018/09/11 · arxiv updated 2018/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Moduli spaces of stable maps to a smooth projective variety typically have several components. We express the virtual class of the moduli space of genus one stable maps to a smooth projective variety as a sum of virtual classes of the components. The key ingredient is a generalised functoriality result for virtual classes. We show that the natural maps from 'ghost' components of the genus one moduli space to moduli spaces of genus zero stable maps satisfy the strong push forward property. As a consequence, we give a cycle-level formula which relates standard and reduced genus one Gromov--Witten invariants of a smooth projective Calabi--Yau theefold.