English

The extended D-Toda hierarchy

Algebraic Geometry 2019-09-30 v1 High Energy Physics - Theory Dynamical Systems

Abstract

In a companion paper to this one, we proved that the Gromov--Witten theory of a Fano orbifold line of type DD is governed by a system of Hirota Bilinear Equations. The goal of this paper is to prove that every solution to the Hirota Bilinear Equations determines a solution to a new integrable hierarchy of Lax equations. We suggest the name extended D-Toda hierarchy for this new system of Lax equations, because it should be viewed as the analogue of Carlet's extended bi-graded Toda hierarchy, which is known to govern the Gromov--Witten theory of Fano orbifold lines of type AA

Cite

@article{arxiv.1909.12735,
  title  = {The extended D-Toda hierarchy},
  author = {Jipeng Cheng and Todor Milanov},
  journal= {arXiv preprint arXiv:1909.12735},
  year   = {2019}
}

Comments

73 pages

R2 v1 2026-06-23T11:28:16.739Z