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arXiv · 1409.4616

Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs

Boris Dubrovin·Si-Qi Liu·Di Yang·Youjin Zhang
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Abstract

For an arbitrary semisimple Frobenius manifold we construct Hodge integrable hierarchy of Hamiltonian partial differential equations. In the particular case of quantum cohomology the tau-function of a solution to the hierarchy generates the intersection numbers of the Gromov--Witten classes and their descendents along with the characteristic classes of Hodge bundles on the moduli spaces of stable maps. For the one-dimensional Frobenius manifold the Hodge hierarchy is a deformation of the Korteweg--de Vries hierarchy depending on an infinite number of parameters. Conjecturally this hierarchy is a universal object in the class of scalar Hamiltonian integrable hierarchies possessing tau-functions.

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Boris Dubrovin, Si-Qi Liu, Di Yang, Youjin Zhang. 2014-09-16. Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs. https://arxiv.org/abs/1409.4616

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