Given a smooth log Calabi–Yau pair (X, D), we use the intrinsic mirror symmetry construction to define the mirror proper Landau–Ginzburg potential and show that it is a generating function of two-point relative Gromov–Witten invariants of (X, D). We compute certain relative invariants with several negative contact orders, and then apply the relative mirror theorem of Fan et al. (Sel Math (NS) 25(4): Art. 54, 25, 2019. https://doi.org/10.1007/s00029-019-0501-z) to compute two-point relative invariants. When D is nef, we compute the proper Landau–Ginzburg potential and show that it is the inverse of the relative mirror map. Specializing to the case of a toric variety X, this implies the conjecture of m Gräfnitz et al. (2022) that the proper Landau–Ginzburg potential is the open mirror map. When X is a Fano variety, the proper potential is related to the anti-derivative of the regularized quantum period.

给定一个光滑的对数 Calabi-Yau 对 ( X ,  D )，我们使用本征镜像对称构造来定义镜像固有的 Landau-Ginzburg 势，并表明它是 ( X的两点相对 Gromov-Witten 不变量) 的生成函数，  D）。我们计算具有几个负接触阶的某些相对不变量，然后应用 Fan 等人的相对镜像定理。（Sel Math (NS) 25(4)：Art. 54, 25, 2019。https://doi.org/10.1007/s00029-019-0501-z）计算两点相对不变量。当D为 nef 时，我们计算适当的 Landau-Ginzburg 势并表明它是相对镜像映射的逆。专门针对环面簇X的情况，这意味着 m Gräfnitz 等人的猜想。(2022) 正确的 Landau-Ginzburg 势是开放镜像图。当X是Fano簇时，本征势与正则化量子周期的反导数有关。