1999/12/23 by Lev Borisov, Lev A. Borisov, Borisov, Lev A. · 1 citation
Mathematics · #14M10 (Primary) 14M25 #17B68 (Secondary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14M10 #msc:14M25 #msc:17B68
paper · pdf · doi:10.48550/arxiv.math/9912195
LaTeX, 15 pages
arxiv created 1999/12/23 · openalex publication_date 1999/12/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this paper is to make the vertex operator algebra approach to mirror symmetry accessible to algebraic geometers. Compared to better-known approaches using moduli spaces of stable maps and special Lagrangian fibrations, this approach follows more closely the original line of thinking that lead to the discovery of mirror symmetry by physicists. The ultimate goal of the vertex algebra approach is to give precise mathematical definitions of N=(2,2) superconformal field theories called A and B models associated to any Calabi-Yau variety and then show that thus constructed theories are related by the mirror involution for all known examples of mirror symmetric varieties.