Invariants of algebraic curves and topological expansion

@inproceedings{Eynard2007InvariantsOA,
title={Invariants of algebraic curves and topological expansion},
author={B. Eynard and N. Orantin},
year={2007}
}

B. Eynard, N. Orantin

Published 2007

For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties. We also study their limits when the curve becomes singular. In addition we find that they can be used to define a formal series, which satisfies formally an Hirota equation, and we thus obtain a new way of constructing a tau function attached to an algebraic curve. These invariants are constructed… CONTINUE READING

2D gravity, matrix models and graph combinatorics”, Lecture given in Les Houches, applications of random matrices in physics, june 2004, mathph/0406013