Invariants of algebraic curves and topological expansion

  title={Invariants of algebraic curves and topological expansion},
  author={Bertrand Eynard and Nicolas Orantin},
  journal={Communications in Number Theory and Physics},
  • B. Eynard, N. Orantin
  • Published 14 February 2007
  • Mathematics
  • Communications in Number Theory and Physics
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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