Mirror symmetry for exceptional unimodular singularities

作者：Li, Changzheng^*; Li, Si; Saito, Kyoji; Shen, Yefeng

来源：Journal of the European Mathematical Society, 2017, 19(4): 1189-1229.

DOI：10.4171/JEMS/691

• Landau-Ginzburg model
• mirror symmetry
• singularity
• FJRW theory
• primitive form

In this paper, we prove the mirror symmetry conjecture between the Saito-Givental theory of exceptional unimodular singularities on the Landau-Ginzburg B-side and the Fan-JarvisRuan-Witten theory of their mirror partners on the Landau-Ginzburg A-side. On the B-side, we develop a perturbative method to compute the genus-0 correlation functions associated to the primitive forms. This is applied to the exceptional unimodular singularities, and we show that the numerical invariants match the orbifold-Grothendieck-Riemann-Roch and WDVV calculations in FJRW theory on the A-side. The coincidence of the full data at all genera is established by reconstruction techniques. Our result establishes the first examples of LG-LG mirror symmetry for weighted homogeneous polynomials of central charge greater than one (i.e. which contain negative degree deformation parameters).

• 出版日期2017
• 单位中山大学; 清华大学