The orbifold quantum cohomology–Jacobian ring correspondence

Let X\mathcal{X} be a Gorenstein toric orbifold, and let WXLFW^{LF}_{\mathcal{X}} be its Lagrangian Floer superpotential. Denote by QHorb(X)QH^*_{\mathrm{orb}}(\mathcal{X}) its orbifold quantum cohomology ring and by Jac(WXLF)Jac(W^{LF}_{\mathcal{X}}) the Jacobian ring of the superpotential. Orbifold Jacobian-ring conjecture. There is an isomorphism

QHorb(X)Jac(WXLF).QH^*_{\mathrm{orb}}(\mathcal{X})\cong Jac(W^{LF}_{\mathcal{X}}).

The analogous isomorphism for toric manifolds was known from work of Fukaya, Oh, Ohta and Ono; the orbifold version was proposed for future investigation and remains open in the source.

Sources & referencesView supporting material

Primary source

Kwokwai Chan, Cheol-Hyun Cho, Siu-Cheong Lau and Hsian-Hua Tseng, “Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds”, arXiv:1208.5282 (2014).

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