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

2009/05/26 by Norbury, Paul · 4 citations
#05A15 #30F30 #32G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0905.4141

Abstract

We prove that the Eynard-Orantin symplectic invariants of the curve xy-y²=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-y²=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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• Counting lattice points in the moduli space of curves
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