String and dilaton equations for counting lattice points in the moduli space of curves
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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.References
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Additional Information
- Paul Norbury
- Affiliation: Department of Mathematics and Statistics, University of Melbourne, Australia 3010
- MR Author ID: 361773
- Email: pnorbury@ms.unimelb.edu.au
- 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.
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 1687-1709
- MSC (2010): Primary 32G15, 30F30, 05A15
- DOI: https://doi.org/10.1090/S0002-9947-2012-05559-0
- MathSciNet review: 3009643