Related papers: McKay correspondence for canonical orders
The classical McKay correspondence establishes an explicit link from the representation theory of a finite subgroup G of SU(2) and the geometry of the minimal resolution of the quotient of the affine plane by G. In this paper we discuss a…
We give a new moduli construction of the minimal resolution of the singularity of type 1/r(1,a) by introducing the Special McKay quiver. To demonstrate that our construction trumps that of the G-Hilbert scheme, we show that the induced…
This paper presents a geometric construction of the McKay-Slodowy correspondence, which extends the classical McKay correspondence. The classical McKay correspondence says: for a finite subgroup G of SL_2(C), there is a bijection between…
In most cases where it had been shown to exist the derived McKay correspondence D(Y) --> D^G(C^n) can be written as a Fourier-Mukai transform which sends point sheaves of the crepant resolution Y to pure sheaves in D^G(C^n). We give a…
Let G be a finite group of automorphisms of a nonsingular complex threefold M such that the canonical bundle omega_M is locally trivial as a G-sheaf. We prove that the Hilbert scheme Y=GHilb M parametrising G-clusters in M is a crepant…
Based on continued fractions with subtractions, we identify the set of real numbers with the set of infinite integer sequences with all terms but the first one greater or equal to two. Each such sequence produces in a canonical way a unique…
We establish a McKay correspondence for finite and linearly reductive subgroup schemes of $\mathrm{SL}_2$ in positive characteristic. As an application, we obtain a McKay correspondence for all rational double point singularities in…
In this paper we show that for any affine complete rational surface singularity there is a correspondence between the dual graph of the minimal resolution and the quiver of the endomorphism ring of the special CM modules. We thus call such…
We construct a noncommutative desingularization of the discriminant of a finite reflection group $G$ as a quotient of the skew group ring $A=S*G$. If $G$ is generated by order two reflections, then this quotient identifies with the…
Consider modular forms arising from a finite-area quotient of the upper-half plane by a Fuchsian group. By the classical results of Kodaira-Spencer, this ring of modular forms may be viewed as the log spin canonical ring of a stacky curve.…
We show that the derived category of coherent sheaves on the quotient stack of the affine plane by a finite small subgroup of the general linear group is obtained from the derived category of coherent sheaves on the minimal resolution by…
We introduce a geometric realization of noncommutative singularity resolutions. To do this, we first present a new conjectural method of obtaining conventional resolutions using coordinate rings of matrix-valued functions. We verify this…
We give an introduction to the McKay correspondence and its connection to quotients of $\mathbb{C}^n$ by finite reflection groups. This yields a natural construction of noncommutative resolutions of the discriminants of these reflection…
Beyond the crucial role they play in the foundations of the theory of overconvergent modular forms, canonical subgroups have found new applications to analytic continuation of overconvergent modular forms. For such applications, it is…
This is the final draft, containing very minor proof-reading corrections. Let G in SL(n,\C) be a finite subgroup and \fie: Y -> X = \C^n/G any resolution of singularities of the quotient space. We prove that crepant exceptional prime…
There are many generalizations of the McKay correspondence for higher dimensional Gorenstein quotient singularities and there are some applications to compute the topological invariants today. But some of the invariants are completely…
The main purpose of this paper is to establish some useful partial resolutions of singularities for pairs from the minimal model theoretic viewpoint. We first establish the existence of log canonical modifications of normal pairs under some…
We give a dual to the McKay correspondence, involving conjugacy classes of subgroups of SU(2). We prove a determinantal formula involving both correspondences. We pose some questions concerning a non-commutative Fourier transform.
In this paper, we consider a generalization of the McKay correspondence in positive characteristic regarding the Euler characteristic of crepant resolutions of quotient singularities given by finite subgroups of the special linear group. As…
Let G be a finite subgroup of SL(n,C). If a quotient variety C^n/G has a crepant resolution, then its Euler number equals to the number of conjugacy classes of G, which is a weak version of the McKay correspondence. In this paper, we…