1304.1632 (Guido Carlet et al.)

Hirota equations for the extended bigraded Toda hierarchy and the total
descendent potential of CP^1 orbifolds    [PDF]

Guido Carlet, Johan van de Leur

We prove that the Hirota quadratic equations of Milanov and Tseng define an integrable hierarchy which is equivalent to the extended bigraded Toda hierarchy. In particular this proves a conjecture of Milanov-Tseng that relates the total descendent potential of the orbifold $C_{k,m}$ with a tau function of the bigraded Toda hierarchy.

View original: http://arxiv.org/abs/1304.1632