Smooth toric G-Hilbert schemes via G-graphs

Abstract

We provide here an infinite family of finite subgroups { G n ⊂ SL n ( C ) } n ⩾ 2 for which the G-Hilbert scheme G n - Hilb A n is a crepant resolution of A n / G n , via the Hilbert–Chow morphism. The proof is based on an explicit description of the toric structure of G n - Hilb A n in terms of Nakamura's G n -graphs. To cite this article: M. Sebestean, C. R. Acad. Sci. Paris, Ser. I 344 (2007).