# Gromov - Witten invariants and integrable hierarchies of topological type

@article{Dubrovin2013GromovW, title={Gromov - Witten invariants and integrable hierarchies of topological type}, author={Boris Dubrovin}, journal={arXiv: Mathematical Physics}, year={2013} }

We outline two approaches to the construction of integrable hierarchies associated with the theory of Gromov - Witten invariants of smooth projective varieties. We argue that a comparison of these two approaches yields nontrivial constraints on Chern numbers of varieties with semisimple quantum cohomology.

## 19 Citations

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. For a smooth projective curve, we derive a closed formula for the generating series of its Gromov–Witten invariants in genus g and degree zero. It is known that the calculation of these invariants…

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