On the genus two free energies for semisimple Frobenius manifolds

@article{Dubrovin2012OnTG,
  title={On the genus two free energies for semisimple Frobenius manifolds},
  author={Boris Dubrovin and Si‐Qi Liu and You-jin Zhang},
  journal={Russian Journal of Mathematical Physics},
  year={2012},
  volume={19},
  pages={273-298}
}
We represent the genus two free energy of an arbitrary semisimple Frobenius manifold as the sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so-called “genus two G-function.” Conjecturally, the genus two G-function vanishes for a series of important examples of Frobenius manifolds associated with simple singularities, as well as for ℙ1-orbifolds with positive Euler characteristics. We explain the reasons for the conjecture and prove it in… 
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