2021/05/09 by Alexander Polishchuk, Umut Varolgunes, Polishchuk, Alexander +1
Mathematics · Physics and Astronomy · #14D05 #14J33 #53D37 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2105.03808
openalex publication_date 2021/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider Takahashi's categorical interpretation of the Berglund-Hubsch mirror symmetry conjecture for invertible polynomials in the case of chain polynomials. Our strategy is based on a stronger claim that the relevant categories satisfy a recursion of directed A∞-categories, which may be of independent interest. We give a full proof of this claim on the B-side. On the A-side we give a detailed sketch of an argument, which falls short of a full proof because of certain missing foundational results in Fukaya-Seidel categories, most notably a generation statement.