Hirota Quadratic Equations for the Gromov--Witten Invariants of ${\mathbb{P}}_{n-2,2,2}^1$

Abstract

Fano orbifold lines are classified by the Dynkin diagrams of type $A,D,$ and $E$. It is known that the corresponding total descendant potential is a tau-function of an appropriate Kac--Wakimoto hierarchy. It is also known that in the A-case the Kac--Wakimoto hierarchies admit an extension and that the total descendant potential is a tau-function of an extended Kac--Wakimoto hierarchy. The goal of this paper is to prove that in the D-case the total descendent potential is also a tau-function of an extended Kac--Wakimoto hierarchy.

37 pages. Some typos and statements are corrected, and the title has been changed

References in corpus (3)

• Gromov--Witten theory of Fano orbifold curves, Gamma integral structures and ADE-Toda Hierarchies
• The Period map for quantum cohomology of ${\mathbb{P}}^2$
• Lectures on Painleve property for semi-simple Frobenius manifolds

Cited by in corpus (1)

• Bilinear equations in Darboux transformations by Boson-Fermion correspondence