2020/12/09 by Veronica Fantini, Fantini, Veronica
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2012.05069
openalex publication_date 2020/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this thesis we study the relation between scattering diagrams and deformations of holomorphic pairs, building on a recent work of Chan--Conan Leung--Ma. The new feature is the extended tropical vertex group where the scattering diagrams are defined. In addition, the extended tropical vertex provides interesting applications: on one hand we get a geometric interpretation of the wall-crossing formulas for coupled 2d-4d systems, previously introduced by Gaiotto--Moore--Neitzke. On the other hand, Gromov--Witten invariants of toric surfaces relative to their boundary divisor appear in the commutator formulas, along with certain absolute invariants due to Gross--Pandharipande--Siebert, which suggests a possible connection to open/closed theories in geometry and mathematical physics.