2022/04/02 by Sam Johnston, Johnston, Sam · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2204.00940
openalex publication_date 2022/04/02 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
For a log Calabi Yau pair (X,D) with X\D smooth affine, satisfying either assumption 1.1 of "The canonical wall structure and intrinsic mirror symmetry" or contains a Zariski dense torus, we prove under the condition that D is the support of a nef divisor, that the structure constants defining a trace form on the mirror algebra constructed by Gross-Siebert are given by the naive curve counts defined by Keel-Yu in definition 1.1 of "The Frobenius structure theorem for log Calabi-Yau varieties containing a torus". As a corollary, we deduce the equality of the mirror algebras constructed by Gross-Siebert and Keel-Yu in the case X\D contains a Zariski dense torus. In addition, we use this result to prove a mirror conjecture proposed by Mandel in "Fano mirror periods from the Frobenius structure conjecture" for Fano pairs satisfying assumption 1.1.