String and dilaton equations for counting lattice points in the moduli space of curves

Norbury, Paul

doi:10.1090/S0002-9947-2012-05559-0

String and dilaton equations for counting lattice points in the moduli space of curves
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Trans. Amer. Math. Soc. 365 (2013), 1687-1709 Request permission

Abstract:

We prove that the Eynard-Orantin symplectic invariants of the curve $xy-y^2=1$ are the orbifold Euler characteristics of the moduli spaces of genus $g$ curves. We do this by associating to the Eynard-Orantin invariants of $xy-y^2=1$ a problem of enumerating covers of the two-sphere branched over three points. This viewpoint produces new recursion relations—string and dilaton equations—between the quasi-polynomials that enumerate such covers.

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