The canonical wall structure and intrinsic mirror symmetry

Abstract As announced in Gross and Siebert (in Algebraic geometry: Salt Lake City 2015, Proceedings of Symposia Pure Mathematics, vol 97, no 2. AMS, Providence, pp 199–230, 2018) 2016, we construct prove consistency the canonical wall structure . This construction starts with a log Calabi–Yau pair ( X , D ) produces structure, as defined et al. (Mem. Amer. Math. Soc. 278(1376), 1376, 1–103, 2022). Roughly put, is data which encodes an algebro-geometric analogue counts Maslov index zero disks. These enumerative invariants are terms punctured Abramovich (Punctured Gromov–Witten invariants, 2020. arXiv:2009.07720v2 [math.AG]). There then two main theorems paper. First, so that, using setup 2022), gives rise to mirror family. Second, that this family coincides intrinsic constructed (Intrinsic symmetry, 2019. arXiv:1909.07649v2 While paper narrower than [math.AG]), it more detailed description mirror.