# Invariants of algebraic curves and topological expansion

@article{Eynard2007InvariantsOA, title={Invariants of algebraic curves and topological expansion}, author={Bertrand Eynard and Nicolas Orantin}, journal={Communications in Number Theory and Physics}, year={2007}, volume={1}, pages={347-452} }

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…

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