Effective determination of quintic FJRW invariants from localization relations

Let Θg,k\Theta_{g,k} denote the FJRW invariants for the quintic indexed by genus gg and kk, and let the relations

bethevirtuallocalizationrelations;assumethenotationandhypothesesofTheorembe the virtual-localization relations; assume the notation and hypotheses of Theorem

. Effective determination conjecture. The equations

using $d_0=0$ and nonempty $\gamma$'s (that is, with markings) give relations that, together with Theorem

, effectively evaluate all Θg,k\Theta_{g,k}. This would provide a method for fully determining all FJRW invariants for the quintic, although the source does not establish that the proposed procedure is effective.

Sources & referencesView supporting material

Primary source

Huai-Liang Chang, Jun Li, Wei-Ping Li and Chiu-Chu Melissa Liu, “A survey on mixed spin P-fields”, arXiv:1603.02092 (2016).

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