Enumerative geometry of Calabi-Yau 4-folds

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dc.creatorKlemm, A.
dc.creatorPandharipande, R.
dc.date2007-02-07
dc.date.accessioned2026-07-07T11:44:16Z
dc.date.available2026-07-07T11:44:16Z
dc.descriptionGromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 4-folds. The main technique is to find exact solutions to moving multiple cover integrals. The resulting invariants are analogous to the BPS counts of Gopakumar and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold invariants to be integers and expect a sheaf theoretic explanation. Several local Calabi-Yau 4-folds are solved exactly. Compact cases, including the sextic Calabi-Yau in CP5, are also studied. A complete solution of the Gromov-Witten theory of the sextic is conjecturally obtained by the holomorphic anomaly equation.
dc.description44 pages
dc.identifierhttps://arxiv.org/abs/math/0702189
dc.identifierhttp://arxiv.org/abs/math/0702189
dc.identifierCommun.Math.Phys.281:621-653,2008
dc.identifierdoi:10.1007/s00220-008-0490-9
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/201544
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.titleEnumerative geometry of Calabi-Yau 4-folds
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