Hurwitz numbers, matrix models and enumerative geometry

Details Hurwitz numbers, matrix models and enumerative geometry Hurwitz numbers, matrix models and enumerative geometry

2007-09-10

arxiv.org/abs/0709.1458v2

In: From Hodge Theory to Integrability and tQFT: tt*-geometry, Proceedings of Symposia in Pure Mathematics, AMS (2008)

Mathematics

Algebraic Geometry

21 pages, 5 figures, small corrections, references added

Scientific paper

We propose a new, conjectural recursion solution for Hurwitz numbers at all genera. This conjecture is based on recent progress in solving type B topological string theory on the mirrors of toric Calabi-Yau manifolds, which we briefly review to provide some background for our conjecture. We show in particular how this B-model solution, combined with mirror symmetry for the one-leg, framed topological vertex, leads to a recursion relation for Hodge integrals with three Hodge class insertions. Our conjecture in Hurwitz theory follows from this recursion for the framed vertex in the limit of infinite framing.

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