KP hierarchy for Hodge integrals

Abstract

Starting from the ELSV formula, we derive a number of new equations on the generating functions for Hodge integrals over the moduli space of complex curves. This gives a new simple and uniform treatment of certain known results on Hodge integrals like Witten's conjecture, Virasoro constrains, Faber's lambda_g conjecture etc. Among other results we show that a properly arranged generating function for Hodge integrals satisfies the equations of the KP hierarchy.

20 pages, 1 figure

References in corpus (2)

• Hurwitz numbers and intersections on moduli spaces of curves
• Gromov-Witten theory, Hurwitz numbers, and Matrix models, I

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