# The Local Gromov–Witten Theory of $${\mathbb{C}\mathbb{P}^1}$$ and Integrable Hierarchies

@article{Brini2010TheLG,
title={The Local Gromov–Witten Theory of \$\$\{\mathbb\{C\}\mathbb\{P\}^1\}\$\$ and Integrable Hierarchies},
author={Andrea Brini},
journal={Communications in Mathematical Physics},
year={2010},
volume={313},
pages={571-605}
}
• A. Brini
• Published 3 February 2010
• Mathematics
• Communications in Mathematical Physics
In this paper we begin the study of the relationship between the local Gromov–Witten theory of Calabi–Yau rank two bundles over the projective line and the theory of integrable hierarchies. We first of all construct explicitly, in a large number of cases, the Hamiltonian dispersionless hierarchies that govern the full-descendent genus zero theory. Our main tool is the application of Dubrovin’s formalism, based on associativity equations, to the known results on the genus zero theory from local…
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