2023/02/06 by Thorgal Hinault, Hinault, Thorgal
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2302.03142
openalex publication_date 2023/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Counts of holomorphic disks are at the heart of the SYZ approach to mirror symmetry. In the non archimedean framework, these counts are expressed as counts of analytic cylinders. In simple cases, such as cluster varieties, these counts can be extracted from a combinatorial algorithm encoded by a scattering diagram. The relevant scattering diagram encodes information about infinitesimal analytic cylinders. In this paper, we give a formula relating counts of a restricted class of cylinders on affine log Calabi Yau surfaces to counts on a single blowup of a toric surface, using non archimedean Gromov Witten theory and a degeneration procedure parametrized by tropical data. This closed form formula constrasts with the scattering diagram approach.