Scalar-flat Kähler orbifolds via quaternionic-complex reduction

Details Scalar-flat Kähler orbifolds via quaternionic-complex reduction Scalar-flat Kähler orbifolds via quaternionic-complex reduction

2009-02-10

arxiv.org/abs/0902.1546v2

Mathematics

Differential Geometry

v2: 16 pages. Some minor alteration

Scientific paper

We prove that any asymptotically locally Euclidean scalar-flat K\"ahler 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.

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