On rational Frobenius manifolds of rank three with symmetries

JOURNAL OF GEOMETRY AND PHYSICS

卷:84

Article

Basalaev, Alexey^1,2  Takahashi, Atsushi³ 

[1] Natl Res Univ, Higher Sch Econ, Moscow 117312, Russia

[2] Leibniz Univ Hannover, D-30167 Hannover, Germany

[3] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5600043, Japan

关键词: Frobenius manifolds;    Singularity theory;    Modular forms;    Elliptic curves;   

DOI  :  10.1016/j.geomphys.2014.05.030

来源: Elsevier

【 摘 要 】

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 K subset of C via the theory of modular forms. By an arithmetic property of an elliptic curve 8, defined over K associated to such a Frobenius manifold, it is proved that there are only two such Frobenius manifolds defined over C satisfying a certain symmetry assumption and thirteen Frobenius manifolds defined over Q satisfying a weak symmetry assumption on the potential. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free