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On rational Frobenius Manifolds of rank three with symmetries

Authors
  • Basalaev, Alexey
  • Takahashi, Atsushi
Type
Preprint
Publication Date
Jan 15, 2014
Submission Date
Jan 15, 2014
Identifiers
DOI: 10.1016/j.geomphys.2014.05.030
Source
arXiv
License
Yellow
External links

Abstract

We study Frobenius manifolds of rank three and dimension one that are related to submanifolds of certain Frobenius manifolds arising in mirror symmetry of elliptic orbifolds. We classify such Frobenius manifolds that are defined over an arbitrary field $\mathbb{K} \subset \mathbb{C}$ via the theory of modular forms. By an arithmetic property of an elliptic curve $\mathbb{E}_\tau$ defined over $\mathbb K$ associated to such a Frobenius manifold, it is proved that there are only two such Frobenius manifolds defined over $\mathbb C$ satisfying a certain symmetry assumption and thirteen Frobenius manifolds defined over $\mathbb Q$ satisfying a weak symmetry assumption on the potential.

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