Proof of a conjecture on the genus two free energy associated to the \(A_n\) singularity. (English) Zbl 1288.53080
Dubrovin, Liu and Zhang conjectured that “If \(M\) is a Frobenius manifold associated to an ADE singularity or an extended affine Weyl group of ADE type, then the genus two \(G\)-function \(G^{(2)}(u,u_{x},u_{xx})\) vanishes.” In this work, the authors prove this conjecture for the class of Frobenius manifolds obtained from the simple singularities of type A.
Reviewer: Vehbi Emrah Paksoy (Fort Lauderdale)
MSC:
| 53D45 | Gromov-Witten invariants, quantum cohomology, Frobenius manifolds |
References:
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