The quantum McKay correspondence for polyhedral singularities
Identifieur interne : 000504 ( Main/Exploration ); précédent : 000503; suivant : 000505The quantum McKay correspondence for polyhedral singularities
Auteurs : Jim Bryan [Canada] ; Amin Gholampour [États-Unis]Source :
- Inventiones mathematicae [ 0020-9910 ] ; 2009-12-01.
Abstract
Abstract: Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura’s G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity ℂ3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be stated as a correspondence: each positive root of R corresponds to one half of a genus zero BPS state. As an application, we use the Crepant Resolution Conjecture to provide a full prediction for the orbifold Gromov-Witten invariants of [ℂ3/G].
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DOI: 10.1007/s00222-009-0212-8
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