Gromov-Witten theory, Hurwitz theory, and completed cycles

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dc.creatorOkounkov, Andrei
dc.creatorPandharipande, Rahul
dc.date2002-04-24
dc.date.accessioned2026-07-07T04:48:04Z
dc.date.available2026-07-07T04:48:04Z
dc.descriptionWe establish an explicit equivalence between the stationary sector of the Gromov-Witten theory of a target curve X and the enumeration of Hurwitz coverings of X in the basis of completed cycles. The stationary sector is formed, by definition, by the descendents of the point class. Completed cycles arise naturally in the theory of shifted symmetric functions. Using this equivalence, we give a complete description of the stationary Gromov-Witten theory of the projective line and elliptic curve. Toda equations for the relative stationary theory of the projective line are derived.
dc.description55 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0204305
dc.identifierhttp://arxiv.org/abs/math/0204305
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63910
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.titleGromov-Witten theory, Hurwitz theory, and completed cycles
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