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arXiv · 1910.03150

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

Jipeng Cheng·Todor Milanov
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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.

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Jipeng Cheng, Todor Milanov. 2019-10-08. Hirota Quadratic Equations for the Gromov--Witten Invariants of $\mathbb{P}_{n-2,2,2}^1$. https://doi.org/10.1016/j.aim.2021.107860

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