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arxiv: math/0101201 · v2 · submitted 2001-01-24 · 🧮 math.AG · math-ph· math.CO· math.MP

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Generating functions for intersection numbers on moduli spaces of curves

Andrei Okounkov
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classification 🧮 math.AG math-phmath.COmath.MP
keywords intersectionfunctionsmathnumbersspacesadlerconnectioncurves
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Using the connection between intersection theory on the Deligne-Mumford spaces and the edge scaling of the GUE matrix model (see math.CO/9903176, math.AG/0101147), we express the n-point functions for the intersection numbers as n-dimensional error-function-type integrals and also give a derivation of Witten's KdV equations using the higher Fay identities of Adler, Shiota, and van Moerbeke.

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