Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy

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dc.creatorMulase, Motohico
dc.creatorSafnuk, Brad
dc.date2006-01-09
dc.date2006-03-04
dc.date.accessioned2026-07-07T06:58:41Z
dc.date.available2026-07-07T06:58:41Z
dc.descriptionWe present in this paper a differential version of Mirzakhani's recursion relation for the Weil-Petersson volumes of the moduli spaces of bordered Riemann surfaces. We discover that the differential relation, which is equivalent to the original integral formula of Mirzakhani, is a Virasoro constraint condition on a generating function for these volumes. We also show that the generating function for psi and kappa_1 intersections on the moduli space of stable algebraic curves is a 1-parameter solution to the KdV hierarchy. It recovers the Witten-Kontsevich generating function when the parameter is set to be 0.
dc.description21 pages, 3 figures; v3. new introduction, minor revisions
dc.identifierhttps://arxiv.org/abs/math/0601194
dc.identifierhttp://arxiv.org/abs/math/0601194
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107455
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectAlgebraic Geometry
dc.titleMirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy
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