On the Genus-One Gromov-Witten Invariants of a Quintic Threefold

Details On the Genus-One Gromov-Witten Invariants of a Quintic Threefold On the Genus-One Gromov-Witten Invariants of a Quintic Threefold

2004-06-06

arxiv.org/abs/math/0406105v2

Mathematics

Algebraic Geometry

55 pages, 5 figures

Scientific paper

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.

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