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arXiv · 2006.16518

A genus-one FJRW invariant via two methods

Jun Li·Wei-Ping Li·Yefeng Shen·Jie Zhou
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Abstract

We calculate a genus-one FJRW invariant of an LG pair $(W_3=x_1^3+x_2^3+x_3^3, \mu_3)$ via two different methods. In the first method, we apply the cosection localization technique to get a genus-one three-spin virtual class explicitly and then calculate the target FJRW invariant via self-intersections of the three-spin virtual class. In the second method, we apply the Mixed Spin P-fields method for the pair and calculate the invariant using the localization formula. This invariant is the building block in establishing the all-genera LG/CY correspondence and its determination enables one to compute the all-genera FJRW invariants for the LG pair.

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Jun Li, Wei-Ping Li, Yefeng Shen, Jie Zhou. 2020-06-30. A genus-one FJRW invariant via two methods. https://doi.org/10.1007/s00209-022-03133-1

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