Abstract
AbstractWe prove that a quotient singularity ℂn/G by a finite subgroup G ⊂ SLn(ℂ) has a crepant resolution only if G is generated by junior elements. This is a generalization of the result of Verbitsky (Asian J. Math.4(3) (2000), 553–563). We also give a procedure to compute the Cox ring of a minimal model of a given ℂn/G explicitly from information of G. As an application, we investigate the smoothness of minimal models of some quotient singularities. Together with work of Bellamy and Schedler, this completes the classification of symplectically imprimitive quotient singularities that admit projective symplectic resolutions.
Publisher
Cambridge University Press (CUP)
Reference33 articles.
1. Crepant Resolutions of a Slodowy Slice in a Nilpotent Orbit Closure in $\mathfrak {sl}_N(\mathbb C)$
2. Shafarevich maps and plurigenera of algebraic varieties
3. M. Donten-Bury and M. Grab , Cox rings of some symplectic resolutions of quotient singularities, arXiv:1504.07463v2.
4. G.-M. Greuel , G. Pfister and H. Schönemann . Singular 3-1-6. A computer algebra system for polynomial computations. (Centre for Computer Algebra, University of Kaiserslautern, 2001). http://www.singular.uni-kl.de
5. Finite Unitary Reflection Groups
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献