Genus-2 \(\operatorname{G}\)-function for \(\mathbb{P}^1\) orbifolds. (English) Zbl 1368.53058
Summary: In this paper we prove that for the Gromov-Witten theory of \(\mathbb{P}^1\) orbifolds of ADE type the genus-2 \(\operatorname{G}\)-function introduced by B. Dubrovin, S. Liu, and Y. Zhang vanishes. Together with our results in a previous paper, this completely solves the main conjecture in their paper. In the process, we also found a sufficient condition for the vanishing of the genus-2 \(\operatorname{G}\)-function which is weaker than the condition given in our previous paper.
MSC:
| 53D45 | Gromov-Witten invariants, quantum cohomology, Frobenius manifolds |
| 14N35 | Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) |
Keywords:
genus-2 \(\operatorname{G}\)-function; Frobenius manifold; \(P^1\) orbifold; cohomological field theoryReferences:
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