Predictions for Gromov-Witten invariants of noncommutative resolutions (Q391039)

The author demonstrates a calculation of the GLSM for \(\mathbb{P}^7[2,2,2,2]\) by using the localization method of [\textit{H.Jockers} et al., Commun. Math. Phys. 325, No. 3, 1139-1170 (2014; Zbl 1301.81253)]. At the nonlinear sigma model phase, the calculation recovers the Gromov-Witten invariants of \(\mathbb{P}^7[2,2,2,2]\). By applying the same method to the Landau-Ginzburg phase, the author makes a prediction for Gromov-Witten invariants of the noncommutative resolution of the branched double cover, which is the Landau-Ginzburg point of the GLSM. The author finds that the results do not match with the Gromov-Witten invariants of a smooth branched double cover and concludes that they are not related by complex structure deformation in the SCFT moduli space.