Revisiting the Classical McKay Correspondence, Derived Equivalences and the Spectrum of Kleinian Surface Singularities: A Look Through the Mirror
Year: 2024
Type: article
Abstract: 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.
Source: Serdica Mathematical Journal
Authors: Enrique Becerra, Ludmil Katzarkov, Ernesto Lupercio
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405719631