Gross and Siebert developed a program for constructing in arbitrary dimension a mirror family to a log Calabi–Yau pair (X, D), consisting of a smooth projective variety X with a normal-crossing anti-canonical divisor D in X. In this paper, we provide an algorithm to practically compute explicit equations of the mirror family in the case when X is obtained as a blow-up of a toric variety along hypersurfaces in its toric boundary, and D is the strict transform of the toric boundary. The main ingredient is the heart of the canonical wall structure associated to such pairs (X, D), which is constructed purely combinatorially, following our previous work with Mark Gross. In the case when we blow up a single hypersurface we show that our results agree with previous results computed symplectically by Aroux–Abouzaid–Katzarkov. In the situation when the locus of blow-up is formed by more than a single hypersurface, due to infinitely many walls interacting, writing the equations becomes significantly more challenging. We provide the first examples of explicit equations for mirror families in such situations.

Gross 和 Siebert 开发了一个程序，用于在任意维度构建一个对数 Calabi-Yau 对 ( X , D ) 的镜像族，由平滑射影簇X和X中的正态交叉反规范除数D组成。在本文中，我们提供了一种算法来实际计算反射镜族的显式方程，其中X是作为复曲面簇沿其复曲面边界中的超曲面的放大而获得的，并且D是复曲面边界的严格变换。主要成分是与这些对（X，D）相关的规范壁结构的核心），它是根据我们之前与 Mark Gross 的合作纯粹组合构建的。在炸毁单个超曲面的情况下，我们表明我们的结果与 Aroux-Abouzaid-Katzarkov 辛计算的先前结果一致。在爆炸轨迹由多个超曲面形成的情况下，由于无限多个壁相互作用，编写方程变得更具挑战性。我们提供了此类情况下镜像族显式方程的第一个示例。