Related papers: Quantum McKay correspondence for disc invariants o…

We announce a result on quantum McKay correspondence for disc invariants of outer legs in toric Calabi-Yau 3-orbifolds, and illustrate our method in a special example $[\mathbb C^3 /\mathbb Z_5 (1, 1, 3)]$.

We prove a comparison formula for curve-counting invariants in the setting of the McKay correspondence, related to the crepant resolution conjecture for Donaldson-Thomas invariants. The conjecture is concerned with comparing the invariants…

The McKay correspondence has had much success in studying resolutions of 3-fold quotient singularities through a wide range of tools coming from geometry, combinatorics, and representation theory. We develop a computational perspective in…

We formulate a Crepant Resolution Correspondence for open Gromov-Witten invariants (OCRC) of toric Calabi-Yau orbifolds by viewing the open theories as sections of Givental's symplectic vector space and the correspondence as a linear map of…

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…

Motivated by physics, we propose two conjectures regarding the cohomology ring of the crepant resolutions of orbifolds and cohomological invariants of K-equivalent manifolds.

We present an algorithm that finds all toric noncommutative crepant resolutions of a given toric 3-dimensional Gorenstein singularity. The algorithm embeds the quivers of these algebras inside a real 3-dimensional torus such that the…

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…

We prove the existence of torus invariant almost complex structure on any positively omnioriented four dimensional primitive quasitoric orbifold. We construct pseudo-holomorphic blowdown maps for such orbifolds. We prove a version of McKay…

In this note, we consider crepant resolutions of the quotient varieties of smooth quintic threefolds by Gorenstein group actions. We compute their Hodge numbers via McKay correspondence. In this way, we find some new pairs…

We prove that every variety with log-terminal singularities admits a crepant resolution by a smooth Artin stack. We additionally prove new McKay correspondences for resolutions by Artin stacks, expressing stringy invariants of…

We formulate a Crepant Resolution Correspondence for open Gromov-Witten invariants (OCRC) of toric Lagrangian branes inside Calabi-Yau 3-orbifolds by encoding the open theories into sections of Givental's symplectic vector space. The…

We propose an arithmetic McKay correspondence which relates suitably defined zeta functions of some Deligne-Mumford stacks to the zeta functions of their crepant resolutions. Some examples are discussed.

Let X/G be a 3-dimensional Calabi-Yau orbifold with codimension 2 singularities. The topology of crepant resolutions of X/G is described by the McKay correspondence (Reid, Ito). We study Calabi-Yau 3-folds Y that arise by deforming the…

Let $G$ be a finite subgroup of $\mathrm{SU}(4)$ whose elements have age not larger than one. In the first part of this paper, we define $K$-theoretic stable pair invariants on the crepant resolution of the affine quotient $\mathbb{C}^4/G$,…

We discuss the resolution of toroidal orbifolds. For the resulting smooth Calabi-Yau manifolds, we calculate the intersection ring and determine the divisor topologies. In a next step, the orientifold quotients are constructed.

The aim of this paper is to study an analog of non-commutative Donaldson-Thomas theory corresponding to the refined topological vertex for small crepant resolutions of toric Calabi-Yau 3-folds. We define the invariants using dimer models…

The derived McKay correspondence conjecture says that there is an equivalence of triangulated categories between the bounded derived categories of commutative and non-commutative crepant resolutions of a Gorenstein singularity. We will…

We compute orbi-disk invariants of compact Gorenstein semi-Fano toric orbifolds by extending the method used for toric Calabi-Yau orbifolds. As a consequence the orbi-disc potential is analytic over complex numbers.

Hypertoric varieties are determined by hyperplane arrangements. In this paper, we use stacky hyperplane arrangements to define the notion of hypertoric Deligne-Mumford stacks. Their orbifold Chow rings are computed. As an application, some…