Russian Journal of Mathematical Physics

, Volume 19, Issue 3, pp 273–298 | Cite as

On the genus two free energies for semisimple Frobenius manifolds

  • Boris Dubrovin
  • Si-Qi Liu
  • Youjin Zhang


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 particular cases.


Weyl Group Dynkin Diagram Dual Graph Quantum Cohomology Integrable Hierarchy 
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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • Boris Dubrovin
    • 1
    • 2
    • 3
  • Si-Qi Liu
    • 4
  • Youjin Zhang
    • 4
  1. 1.SISSATriesteItaly
  2. 2.Laboratory of Geometric Methods in Mathematical PhysicsMoscow State UniversityMoscowRussia
  3. 3.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  4. 4.Department of Mathematical SciencesTsinghua UniversityBeijingP. R. China

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