Strominger–Yau–Zaslow geometry, Affine Spheres and Painlevé III

Abstract

We give a gauge invariant characterisation of the elliptic affine sphere equation and the closely related Tzitzéica equation as reductions of real forms of SL(3,C) anti–self–dual Yang–Mills equations by two translations, or equivalently as a special case of the Hitchin equation. We use the Loftin–Yau–Zaslow construction to give an explicit expression for a… (More)

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