Abstract
We propose a new higher dimensional version of the McKay correspondence which enables us to understand the “Hodge numbers” assigned to singular Gorenstein varieties by physicists. Our results lead to the conjecture that string theory indicates the existence of some new cohomology theory H st ∗(X) for algebraic varieties with Gorenstein singularities. We give a formal mathematical definition of the Hodge numbers h st p, q ( X) inspired from the consideration of strings on orbifolds and from this new (conjectural) version of the McKay correspondence. The numbers h st p, q ( X) are expected to give the spectrum of orbifoldized Landau-Ginzburg models and mirror duality relations for higher dimensional Calabi-Yau varieties with Gorenstein toroidal or quotient singularities.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
