Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 32G15, 30F30, 05A15

Retrieve articles in all journals with MSC (2010): 32G15, 30F30, 05A15


Additional Information

Paul Norbury
Affiliation: Department of Mathematics and Statistics, University of Melbourne, Australia 3010
Email: pnorbury@ms.unimelb.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05559-0
PII: S 0002-9947(2012)05559-0
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.