KP hierarchy for Hodge integrals

Details KP hierarchy for Hodge integrals KP hierarchy for Hodge integrals

2008-09-18

arxiv.org/abs/0809.3263v1

Mathematics

Algebraic Geometry

20 pages, 1 figure

Scientific paper

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.

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