%0 Journal Article
%J Russian Journal of Mathematical Physics. Volume 19, Issue 3, September 2012, Pages 273-298
%D 2012
%T On the genus two free energies for semisimple Frobenius manifolds
%A Boris Dubrovin
%A Si-Qi Liu
%A Youjin Zhang
%X We 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.
%B Russian Journal of Mathematical Physics. Volume 19, Issue 3, September 2012, Pages 273-298
%I SISSA
%G en
%U http://hdl.handle.net/1963/6464
%1 6411
%2 Mathematics
%4 1
%# MAT/07 FISICA MATEMATICA
%$ Submitted by Boris Dubrovin (dubrovin@sissa.it) on 2013-02-08T11:35:38Z\\nNo. of bitstreams: 1\\n1205.5990v1.pdf: 547320 bytes, checksum: 9c9d894fbe3241c632b6cab13379f9c9 (MD5)
%R 10.1134/S1061920812030028