Scalar-flat Kähler Orbifolds via Quaternionic-complex Reduction
نویسنده
چکیده
We prove that any asymptotically locally Euclidean scalar-flat Kähler 4-orbifold whose isometry group contains a 2-torus is isometric, up to an orbifold covering, to a quaternionic-complex quotient of a k-dimensional quaternionic vector space by a (k − 1)-torus. In order to do so, we first prove that any compact anti-self-dual 4-orbifold with positive Euler characteristic whose isometry group contains a 2-torus is conformally equivalent, up to an orbifold covering, to a quaternionic quotient of k-dimensional quaternionic projective space by a (k − 1)-torus.
منابع مشابه
Quaternionic Kähler Reductions of Wolf Spaces
The main purpose of the following article is to introduce a Lie theoretical approach to the problem of classifying pseudo quaternionic-Kähler (QK) reductions of the pseudo QK symmetric spaces, otherwise called generalized Wolf spaces. The history of QK geometry starts with the celebrated Berger’s Theorem [Ber55] which classifies all the irreducible holonomy groups for not locally symmetric pseu...
متن کاملMarsden-Weinstein Reductions for Kähler, Hyperkähler and Quaternionic Kähler Manifolds
If a Lie group G acts on a symplectic manifold (M, ω) and preserves the symplectic form ω, then in some cases there may exist a moment map ([C]) Φ from M to the dual of the Lie algebra. When the action is (locally) free, the preimage of a point in the dual of the Lie algebra modulo the isotropy group of this point will still be a symplectic manifold (orbifold). This process is called the Marsde...
متن کاملLinear perturbations of quaternionic metrics II. The quaternionic-Kähler case
We extend the twistor methods developed in our earlier work on linear deformations of hyperkähler manifolds [1] to the case of quaternionic-Kähler manifolds. Via Swann’s construction, deformations of a 4d-dimensional quaternionic-Kähler manifold M are in one-to-one correspondence with deformations of its 4d+ 4-dimensional hyperkähler cone S. The latter can be encoded in variations of the comple...
متن کاملA rigidity theorem for quaternionic Kähler structures
We study the moduli space of quaternionic Kähler structures on a compact manifold of dimension 4n ≥ 12 from a point of view of Riemannian geometry, not twistor theory. Then we obtain a rigidity theorem for quaternionic Kähler structures of nonzero scalar curvature by observing the moduli space.
متن کاملWeighted projective embeddings, stability of orbifolds and constant scalar curvature Kähler metrics
We embed polarised orbifolds with cyclic stabiliser groups into weighted projective space via a weighted form of Kodaira embedding. Dividing by the (non-reductive) automorphisms of weighted projective space then formally gives a moduli space of orbifolds. We show how to express this as a reductive quotient and so a GIT problem, thus defining a notion of stability for orbifolds. We then prove an...
متن کامل