2024/07/31 by Enrique Becerra, Ludmil Katzarkov, Becerra, Enrique +3
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2407.21313
openalex publication_date 2024/07/31 · openalex created_date 2024/08/04 · openalex updated_date 2026/07/28
In this article, we revisit the classical McKay correspondence via homological mirror symmetry. Specifically, we demonstrate how this correspondence can be articulated as a derived equivalence between the category of vanishing cycles associated with a Kleinian surface singularity and the category of perfect complexes on the corresponding quotient orbifold. We further illustrate how this equivalence allows for the interpretation of the spectrum of a Kleinian surface singularity solely in terms of the representation-theoretic data of the associated binary polyhedral group.