Related papers: Arithmetic McKay correspondence
A formula for calculating the Lefschetz number of an automorphism acting on a crepant resolution for a quotient of a Kahler manifold derived from an equivariant version of McKay correspondence. The latter is proven in some cases. As an…
We describe the derived McKay correspondence for real reflection groups of rank $3$ in terms of a maximal resolution of the logarithmic pair consisting of the quotient variety and the discriminant divisor with coefficient $\frac{1}{2}$. As…
The deformation approach of arXiv:2104.07816 for computing zeta functions of one-parameter Calabi-Yau threefolds is generalised to cover also multiparameter manifolds. Consideration of the multiparameter case requires the development of an…
This paper establishes new bridges between number theory and modern harmonic analysis, namely between the class of complex functions, which contains zeta functions of arithmetic schemes and closed with respect to product and quotient, and…
We study the images of tautological bundles on Hilbert schemes of points on surfaces and their wedge powers under the derived McKay correspondence. The main observation of the paper is that using a derived equivalence differing slightly…
This is a rough write-up of my lecture at Kinosaki and two lectures at RIMS workshops in Dec 1996, on work in progress that has not yet reached any really worthwhile conclusion, but contains lots of fun calculations. History of Vafa's…
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 article, we study the multiple zeta functions (MZF) and some of its variants at identical arguments. Using the harmonic product, these functions can be expressed as polynomials in the Riemann zeta function. Firstly, we note that an…
We revisit the classical two-dimensional McKay correspondence in two respects: The first one, which is the main point of this work, is that we take into account of the multiplicative structure given by the orbifold product; second, instead…
We examine "partition zeta functions" analogous to the Riemann zeta function but summed over subsets of integer partitions. We prove an explicit formula for a family of partition zeta functions already shown to have nice properties -- those…
The spectral zeta function of the Laplacian on self-similar fractal sets has been previously studied and shown to meromorphically extend to the complex plane. In this work we establish under certain conditions a relationship between the…
We give some necessary conditions for the existence of a symplectic resolution for quotient singularities. The McKay correspondence is also worked out for these resolutions.
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…
In the paper, we give partition-theoretic results for the coefficients of some mock theta functions and prove their congruence properties. Some recurrence relations connecting the coefficients of the mock theta functions with certain…
The Markov-Dyck shifts arise from finite directed graphs. An expression for the zeta function of a Markov-Dyck shift is given. The derivation of this expression is based on a formula in Keller (G. Keller, {\it Circular codes, loop counting,…
Let $\pi\colon Y\to X$ denote the canonical resolution of the two dimensional Kleinian singularity $X$ of type ADE. In the present paper, we establish isomorphisms between the cohomological and K-theoretical Hall algebras of…
This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that…
The purpose of this work is to study in the case of function fields and rank-$n$, certain correspondences associated with Jacobi sums in a Coleman's work.
Given a brane tiling, that is, a bipartite graph on a torus, we can associate with it a singular 3-Calabi-Yau variety. In this paper we study its commutative and non-commutative crepant resolutions. We give an explicit toric description of…
In this paper, we study the relation between the zeta function of a Calabi-Yau hypersurface and the zeta function of its mirror. Two types of arithmetic relations are discovered. This motivates us to formulate two general arithmetic mirror…