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A hyper-Kähler Fourier transform. (English) Zbl 0951.32018

Authors’ abstract: “Given two hyper-Kähler manifolds \(X\) and \(Y\) and a quaternionic instanton on \(X\times Y\), one can define a Fourier-Mukai transform, which maps quaternionic instantons on \(X\) to quaternionic instantons on \(Y\). This encompasses the cases of two-dimensional algebraic tori and \(K3\) surfaces treated elsewhere. Some higher dimensional examples are given”.

MSC:

32Q15 Kähler manifolds
14J28 \(K3\) surfaces and Enriques surfaces
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
32L25 Twistor theory, double fibrations (complex-analytic aspects)
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