A_{n-1} singularities and nKdV hierarchies

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dc.creatorGivental, Alexander
dc.date2002-09-16
dc.date2003-05-28
dc.date.accessioned2026-07-07T04:50:56Z
dc.date.available2026-07-07T04:50:56Z
dc.descriptionAccording to a conjecture of E. Witten proved by M. Kontsevich, a certain generating function for intersection indices on the Deligne -- Mumford moduli spaces of Riemann surfaces coincides with a certain tau-function of the KdV hierarchy. The generating function is naturally generalized under the name the {\em total descendent potential} in the theory of Gromov -- Witten invariants of symplectic manifolds. The papers arXiv: math.AG/0108100 and arXive: math.DG/0108160 contain two equivalent constructions, motivated by some results in Gromov -- Witten theory, which associate a total descendent potential to any semisimple Frobenius structure. In this paper, we prove that in the case of K.Saito's Frobenius structure on the miniversal deformation of the $A_{n-1}$-singularity, the total descendent potential is a tau-function of the $n$KdV hierarchy. We derive this result from a more general construction for solutions of the $n$KdV hierarchy from $n-1$ solutions of the KdV hierarchy.
dc.description29 pages, to appear in Moscow Mathematical Journal
dc.identifierhttps://arxiv.org/abs/math/0209205
dc.identifierhttp://arxiv.org/abs/math/0209205
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64968
dc.subjectAlgebraic Geometry
dc.subjectMathematical Physics
dc.subjectRepresentation Theory
dc.subject14N35; 17B69; 32S30; 37K30
dc.titleA_{n-1} singularities and nKdV hierarchies
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