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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)



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

Author: Paul Norbury
Journal: Trans. Amer. Math. Soc. 365 (2013), 1687-1709
MSC (2010): Primary 32G15, 30F30, 05A15
Published electronically: September 25, 2012
MathSciNet review: 3009643
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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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Additional Information

Paul Norbury
Affiliation: Department of Mathematics and Statistics, University of Melbourne, Australia 3010

Received by editor(s): June 11, 2010
Received by editor(s) in revised form: September 20, 2010, and February 4, 2011
Published electronically: September 25, 2012
Additional Notes: The author was partially supported by ARC Discovery project DP1094328.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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