Compact anti-self-dual orbifolds with torus actions |
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Authors: | Dominic Wright |
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Institution: | 1. Department of Mathematics, Imperial College, London, UK
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Abstract: | We give a classification of toric anti-self-dual conformal structures on compact 4-orbifolds with positive Euler characteristic.
Our proof is twistor theoretic: the interaction between the complex torus orbits in the twistor space and the twistor lines
induces meromorphic data, which we use to recover the conformal structure. A compact anti-self-dual orbifold can also be constructed
by adding a point at infinity to an asymptotically locally Euclidean (ALE) scalar-flat K?hler orbifold. We use this observation
to classify ALE scalar-flat K?hler 4-orbifolds whose isometry group contain a 2-torus. |
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