2004/06/06 by Jun Li, Li, Jun, Aleksey Zinger +1
Mathematics · #14N35 #53D45 #Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.AG #math.SG #msc:14N35 #msc:53D45
paper · pdf · doi:10.48550/arxiv.math/0406105
55 pages, 5 figures
arxiv created 2005/07/05 · arxiv updated 2009/12/01
We rederive a relation between the genus-one GW-invariants of a quintic threefold in \Pf and the genus-zero and genus-one GW-invariants of \Pf. In contrast to the more general derivation in a separate paper, the present derivation relies on a widely believed, but still unproven, statement concerning rigidity of holomorphic curves in Calabi-Yau threefolds. On the other hand, this paper's derivation is more direct and geometric. It requires a bit more effort, but relies on less outside work.