00982nas a2200133 4500008004100000245007000041210006300111260001000174520057500184100002000759700001500779700001800794856003600812 2012 en d00aOn the genus two free energies for semisimple Frobenius manifolds0 agenus two free energies for semisimple Frobenius manifolds bSISSA3 aWe represent the genus two free energy of an arbitrary semisimple Frobenius\\r\\nmanifold as a sum of contributions associated with dual graphs of certain\\r\\nstable algebraic curves of genus two plus the so-called \\\"genus two G-function\\\".\\r\\nConjecturally the genus two G-function vanishes for a series of important\\r\\nexamples of Frobenius manifolds associated with simple singularities as well as\\r\\nfor ${\\\\bf P}^1$-orbifolds with positive Euler characteristics. We explain the\\r\\nreasons for such Conjecture and prove it in certain particular cases.1 aDubrovin, Boris1 aLiu, Si-Qi1 aZhang, Youjin uhttp://hdl.handle.net/1963/6464