Kavli Affiliate: Todor Milanov
| Summary:
We prove that the Gromov–Witten invariants of the elliptic orbifold lines $mathbfP^1_3,3,3$, $mathbfP^1_2,4,4$, and $mathbfP^1_2,3,6$ satisfy a certain system of Hirota Quadratic (or Bilinear) Equations. Our result is the analogue of the so-called Toda conjecture in the Gromov-Witten theory of $mathbfP^1$ or more precisely its non-extended version. A new feature in our constructions is a certain bilinear operator whose principal symbol can be expressed in terms of elliptic theta functions.
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