Scalar-flat Kähler orbifolds via quaternionic-complex reduction

Abstract

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.

v2: 16 pages. Some minor alteration

References in corpus (2)

• Toric selfdual Einstein metrics on compact orbifolds
• Compact anti-self-dual orbifolds with torus actions