English

A genus-one FJRW invariant via two methods

Algebraic Geometry 2023-04-12 v2

Abstract

We calculate a genus-one FJRW invariant of an LG pair (W3=x13+x23+x33,μ3)(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.

Cite

@article{arxiv.2006.16518,
  title  = {A genus-one FJRW invariant via two methods},
  author = {Jun Li and Wei-Ping Li and Yefeng Shen and Jie Zhou},
  journal= {arXiv preprint arXiv:2006.16518},
  year   = {2023}
}

Comments

24 pages, 7 figures, minor changes

R2 v1 2026-06-23T16:43:24.198Z