# Gromov-Witten theory of orbicurves, the space of tri-polynomials and symplectic field theory of Seifert fibrations

@article{Rossi2008GromovWittenTO, title={Gromov-Witten theory of orbicurves, the space of tri-polynomials and symplectic field theory of Seifert fibrations}, author={Paolo Rossi}, journal={Mathematische Annalen}, year={2008}, volume={348}, pages={265-287} }

We compute, with symplectic field theory (SFT) techniques, the Gromov-Witten theory of $${\mathbb{P}^1_{\alpha_1,\ldots,\alpha_a}}$$, i.e., the complex projective line with a orbifold points. A natural subclass of these orbifolds, the ones with polynomial quantum cohomology, gives rise to a family of (polynomial) Frobenius manifolds and integrable systems of Hamiltonian PDEs, which extend the (dispersionless) bigraded Toda hierarchy (Carlet, The extended bigraded toda hierarchy. arXiv preprint…

## 45 Citations

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