Related papers: On the QALE geometry of Nakajima's metric

Using an approach developed by Melrose to study the geometry at infinity of the Nakajima metric on the reduced Hilbert scheme of points on $\mathbb{C}^2$, we show that the Nakajima metric on a quiver variety is quasi-asymptotically conical…

This is the sequel to "Asymptotically Locally Euclidean metrics with holonomy SU(m)", math.AG/9905041. Let G be a subgroup of U(m), and X a resolution of C^m/G. We define a special class of Kahler metrics g on X called Quasi Asymptotically…

Let G be a nontrivial finite subgroup of U(m) acting freely on C^m - 0. Then C^m/G has an isolated quotient singularity at 0. Let X be a resolution of C^m/G, and g a Kahler metric on X. We say that g is Asymptotically Locally Euclidean…

We construct new examples of quasi-asymptotically conical (QAC) Calabi-Yau manifolds that are not quasi-asymptotically locally Euclidean (QALE). We do so by first providing a natural compactification of QAC-spaces by manifolds with fibred…

We show that any asymptotically locally Euclidean (ALE) metric which is obstruction-flat or extended obstruction-flat must be ALE of a certain optimal order. Moreover, our proof applies to very general elliptic systems and in any dimension…

This paper is based on a talk at the conference `The McKay correspondence, mutation and related topics' from July 2020. We provide an introduction to joint work of the author with S{\o}ren Gammelgaard, \'{A}d\'{a}m Gyenge and Bal\'{a}zs…

In this paper we apply the hyper-K\"ahler quotient construction to Lie groups with a left invariant hyper-K\"ahler structure under the action of a closed abelian subgroup by left multiplication. This is motivated by the fact that some known…

Firstly, we pursue the work of W. Cherry on the analogue of the Kobayashi semi distance dCK that he introduced for analytic spaces defined over a non-Archimedean metrized field k. We prove various characterizations of smooth projective…

We consider the mapping properties of generalized Laplace-type operators ${\mathcal L} = \nabla^* \nabla + {\mathcal R}$ on the class of quasi-asymptotically conical (QAC) spaces, which provide a Riemannian generalization of the QALE…

We present a method in nonlinear elliptic systems to study curvature decays on asymptotically locally Euclidean (ALE) manifolds. In particular, we show that scalar flat Kahler and harmonic ALE metrics of real dimension n are of order n-2.

We construct a hyperk\"ahler metric on twisted cotangent bundles of the complex projective space $\mathbb{CP}^n$ explicitly in terms of local coordinates. Note that the twisted cotangent bundles of $\mathbb{CP}^n$ are holomorphically…

On an almost complex manifold $(M,J)$, a pluricanonical locally conformally almost K\"ahler (LCAK) metric $g$ is induced by a locally conformally symplectic structure $(F,\theta)$ of the first kind, characterized by the fact that $D\theta$…

We study transverse equivariant Hilbert schemes of affine hypertoric varieties equipped with a symplectic action of a Weyl group. In particular, we show that the Coulomb branches of Braverman, Finkelberg, and Nakajima can be obtained either…

We prove that a certain class of ALE spaces always has a Kahler conformal compactification, and moreover provide explicit formulas for the conformal factor and the Kahler potential of said compactification. We then apply this to give a new…

For a finite subgroup $\Gamma\subset \mathrm{SL}(2,\mathbb{C})$ and $n\geq 1$, we construct the (reduced scheme underlying the) Hilbert scheme of $n$ points on the Kleinian singularity $\mathbb{C}^2/\Gamma$ as a Nakajima quiver variety for…

We solve the geodesic equation in the space of K\"ahler metrics under the setting of asymptotically locally Euclidean (ALE) K\"ahler manifolds and we prove global $\mathcal{C}^{1,1}$ regularity of the solution. Then, we relate the solution…

We prove a novel action of the (three-dimensional) Heisenberg algebra on the equivariant K-theory of the Hilbert scheme of points on C2. These operators are defined via pushforwards and pullbacks via the Nakajima correspondences while…

We define Discrete Quasi-Einstein metrics (DQE-metrics) as the critical points of discrete total curvature functional on triangulated 3-manifolds. We study DQE-metrics by introducing some combinatorial curvature flows. We prove that these…

Joyce structures were introduced by T. Bridgeland in the context of the space of stability conditions of a three-dimensional Calabi-Yau category and its associated Donaldson-Thomas invariants. In subsequent work, T. Bridgeland and I.…

The quasi-quantized Hall effect (QQHE) is the three-dimensional (3D) counterpart of the integer quantum Hall effect (QHE),exhibited only by two-dimensional (2D) electron systems. It has recently been observed in layered materials,…