The Toda equations and the Gromov-Witten theory of the Riemann sphere

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dc.creatorPandharipande, R.
dc.date1999-12-20
dc.date.accessioned2026-07-07T05:32:23Z
dc.date.available2026-07-07T05:32:23Z
dc.descriptionConsequences of the Toda equations arising from the conjectural matrix model for the Riemann sphere are investigated. The Toda equations determine the Gromov-Witten descendent potential (including all genera) of the Riemann sphere from the degree 0 part. Degree 0 series computations via Hodge integrals then lead to higher degree predictions by the Toda equations. First, closed series forms for all 1-point invariants of all genera and degrees are given. Second, degree 1 invariants are investigated with new applications to Hodge integrals. Third, a differential equation for the generating function of the classical simple Hurwitz numbers (in all genera and degrees) is found -- the first such equation. All these results depend upon the conjectural Toda equations. Finally, proofs of the Toda equations in genus 0 and 1 are given.
dc.description16 pages, LaTeX2e
dc.identifierhttps://arxiv.org/abs/math/9912166
dc.identifierhttp://arxiv.org/abs/math/9912166
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79642
dc.subjectAlgebraic Geometry
dc.titleThe Toda equations and the Gromov-Witten theory of the Riemann sphere
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