The Reduced Genus-One Gromov-Witten Invariants of Calabi-Yau Hypersurfaces

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dc.creatorZinger, Aleksey
dc.date2007-05-16
dc.date2008-09-23
dc.date.accessioned2026-07-07T10:04:08Z
dc.date.available2026-07-07T10:04:08Z
dc.descriptionWe compute the reduced genus 1 Gromov-Witten invariants of Calabi-Yau hypersurfaces. As a consequence, we confirm the 1993 Bershadsky-Cecotti Ooguri-Vafa (BCOV) prediction for the standard genus 1 GW-invariants of a quintic threefold. We combine constructions from a series of previous papers with the classical localization theorem to relate the reduced genus 1 invariants of a CY-hypersurface to previously computed integrals on moduli spaces of stable genus 0 maps into projective space. The resulting, rather unwieldy, expressions for a genus 1 equivariant generating function simplify drastically, using a regularity property of a genus 0 equivariant generating function in half of the cases. Finally, by disregarding terms that cannot effect the non-equivariant part of the former, we relate the answer to an explicit hypergeometric series in a simple way. The approach described in this paper is systematic. It is directly applicable to computing reduced genus 1 GW-invariants of other complete intersections and should apply to higher-genus localization computations.
dc.description48 pages, 5 figures; exposition modified and a few typos corrected
dc.identifierhttps://arxiv.org/abs/0705.2397
dc.identifierhttp://arxiv.org/abs/0705.2397
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169554
dc.subjectAlgebraic Geometry
dc.subjectSymplectic Geometry
dc.subject14N35, 53D45
dc.titleThe Reduced Genus-One Gromov-Witten Invariants of Calabi-Yau Hypersurfaces
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