Hirota equations for the extended bigraded Toda hierarchy and the total descendent potential of CP¹ orbifolds

2013/04/05 by Guido Carlet, Johan van de Leur · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1088/1751-8113/46/40/405205

published as J. Phys. A: Math. Theor. 46 (2013) 405205 · 17 pages

arxiv created 2013/04/05 · arxiv updated 2013/09/25

Abstract

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.

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• On Gromov--Witten invariants of ℙ¹-orbifolds and topological difference equations